Ruiz Baier | Publications

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Ricardo Ruiz Baier

School of Mathematics, Monash University
Office 315, 9 Rainforest Walk
Melbourne, VIC 3800, Australia
E-mail: Ricardo.RuizBaier@monash.edu
Phone: +61 3 9905 4485

PUBLICATIONS

Under review (submitted preprints)

[7]	Z. Gharibi, M. Dehghan, and R. Ruiz-Baier A stabilization-free mixed virtual element approximation for unsteady non-Newtonian pseudoplastic Stokes flows. 2024. [ DOI \| arXiv \| .pdf ]
[6]	S. Kumar, U. Rajput, and R. Ruiz-Baier Mixed virtual element methods for a stress-velocity-rotation formulation in viscoelasticity. 2024. [ DOI \| arXiv \| .pdf ]
[5]	A. Khan, B. P. Lamichhane, R. Ruiz-Baier, and S. Villa-Fuentes A priori and a posteriori error bounds for the fully mixed FEM formulation of poroelasticity with stress-dependent permeability. 2024. [ DOI \| arXiv \| .pdf ]
[4]	M. Álvarez, G. A. Benavides, G. N. Gatica, E. Henriquez, and R. Ruiz-Baier Banach spaces-based mixed finite element methods for a steady sedimentation-consolidation system. 2024. [ http ]
[3]	A. Bansal, N. A. Barnafi, D. N. Pandey, and R. Ruiz-Baier A Lagrange multiplier-based method for Stokes-linearized poro-hyperelastic interface problems. 2024. [ DOI \| arXiv \| .pdf ]
[2]	R. Demos, R. Dubey, R. Ruiz-Baier, and S. Villa-Fuentes Numerical analysis of a porous natural convection system with vorticity and viscous dissipation. 2024. [ DOI \| arXiv \| .pdf ]
[1]	A. Khan, D. Mora, R. Ruiz-Baier, and J. Vellojin Divergence-conforming finite element methods for flow-transport coupling with osmotic effects. 2024. [ DOI \| arXiv \| .pdf ]

In press (accepted for publication)

[2]	N. Nataraj, R. Ruiz-Baier, and A. Yousuf Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem. Computational Methods in Applied Mathematics, 2025. [ bib \| DOI \| .pdf ]
[1]	J. Careaga, G. N. Gatica, C. Inzunza, and R. Ruiz-Baier New Banach spaces-based mixed finite element methods for the coupled poroelasticity and heat equations. IMA Journal of Numerical Analysis, 2024. [ bib \| DOI \| .pdf ]

Published in refereed international journals

[122]	G. N. Gatica, C. Inzunza, and R. Ruiz-Baier Primal-mixed finite element methods for the coupled Biot and Poisson–Nernst–Planck equations. Computers & Mathematics with Applications, 186:53–83, 2025. [ bib \| DOI \| .pdf ]
[121]	R. Khot, D. Mora, and R. Ruiz-Baier Virtual element methods for Biot–Kirchhoff poroelasticity. Mathematics of Computation, 94(353):1101–1146, 2025. [ bib \| DOI \| .pdf ]
[120]	R. Khot, A. E. Rubiano, and R. Ruiz-Baier Robust virtual element methods for coupled stress-assisted diffusion problems. SIAM Journal on Scientific Computing, 47(1):A497–A526, 2025. [ bib \| DOI \| .pdf ]
[119]	S. Badia, M. Hornkjøl, A. Khan, K.-A. Mardal, A. F. Martín, and R. Ruiz-Baier Efficient and reliable divergence-conforming methods for an elasticity-poroelasticity interface problem. Computers & Mathematics with Applications, 157:173–194, 2024. [ bib \| DOI \| .pdf ]
[118]	R. Bürger, A. Khan, P. E. Méndez, and R. Ruiz-Baier Divergence-conforming methods for transient doubly-diffusive flows: A priori and a posteriori error analysis. IMA Journal of Numerical Analysis, 44(6):3520–3572, 2024. [ bib \| DOI \| .pdf ]
[117]	R. Caraballo, C. W. In, A. F. Martín, and R. Ruiz-Baier Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form. Numerical Methods for Partial Differential Equations, 40(3):e23083(1–26), 2024. [ bib \| DOI \| .pdf ]
[116]	C. I. Correa, G. N. Gatica, E. Henríquez, R. Ruiz-Baier, and M. Solano Banach spaces-based mixed finite element methods for the coupled Navier–Stokes and Poisson–Nernst–Planck equations. Calcolo, 61:e31(1–44), 2024. [ bib \| DOI \| .pdf ]
[115]	S. Kumar, D. Mora, R. Ruiz-Baier, and N. Verma Numerical solution of the Biot/elasticity interface problem using virtual element methods. Journal of Scientific Computing, 98:e53(1–32), 2024. [ bib \| DOI \| .pdf ]
[114]	B. P. Lamichhane, R. Ruiz-Baier, and S. Villa-Fuentes New twofold saddle-point formulations for Biot poroelasticity with porosity-dependent permeability. Results in Applied Mathematics, 21:e100438(1–22), 2024. [ bib \| DOI \| .pdf ]
[113]	V. Anaya, R. Caraballo, S. Caucao, L. F. Gatica, R. Ruiz-Baier, and I. Yotov A vorticity-based mixed formulation for the unsteady Brinkman–Forchheimer equations. Computer Methods in Applied Mechanics and Engineering, 404:e115829(1–30), 2023. [ bib \| DOI \| .pdf ]
[112]	V. Anaya, R. Caraballo, R. Ruiz-Baier, and H. Torres On augmented finite element formulations for the Navier–Stokes equations with vorticity and variable viscosity. Computers & Mathematics with Applications, 143:397–416, 2023. [ bib \| DOI \| .pdf ]
[111]	C. I. Correa, G. N. Gatica, and R. Ruiz-Baier New mixed finite element methods for the coupled Stokes/ Poisson–Nernst–Planck equations in Banach spaces. ESAIM: Mathematical Modelling and Numerical Analysis, 57:1511–1551, 2023. [ bib \| DOI \| .pdf ]
[110]	M. Dehghan, Z. Gharibi, and R. Ruiz-Baier Optimal error estimates of coupled and divergence-free virtual element methods for the Poisson–Nernst–Planck/Navier–Stokes equations and applications in electrochemical systems. Journal of Scientific Computing, 94:e72(1–50), 2023. [ bib \| DOI \| .pdf ]
[109]	G. N. Gatica, N. Núñez, and R. Ruiz-Baier Mixed-primal methods for natural convection driven phase change with Navier–Stokes–Brinkman equations. Journal of Scientific Computing, 95:e79(1–38), 2023. [ bib \| DOI \| .pdf ]
[108]	G. N. Gatica, N. Núñez, and R. Ruiz-Baier New non-augmented mixed finite element methods for the Navier–Stokes–Brinkman equations using Banach spaces. Journal of Numerical Mathematics, 31(4):343–373, 2023. [ bib \| DOI \| .pdf ]
[107]	B. Gómez-Vargas, K.-A. Mardal, R. Ruiz-Baier, and V. Vinje Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion. SIAM Journal on Numerical Analysis, 63(3):1449–1481, 2023. [ bib \| DOI \| .pdf ]
[106]	S. Meddahi and R. Ruiz-Baier A mixed discontinuous Galerkin method for a linear viscoelasticity problem with strongly imposed symmetry. SIAM Journal on Scientific Computing, 45(1):B27–B56, 2023. [ bib \| DOI \| .pdf ]
[105]	V. Anaya, A. Khan, D. Mora, and R. Ruiz-Baier Robust a posteriori error analysis for rotation-based formulations of the elasticity/poroelasticity coupling. SIAM Journal on Scientific Computing, 44(4):B964–B995, 2022. [ bib \| DOI \| .pdf ]
[104]	V. Anaya, D. Mora, A. K. Pani, and R. Ruiz-Baier Error analysis for a vorticity/Bernoulli pressure formulation for the Oseen equations. Journal of Numerical Mathematics, 30(3):209–230, 2022. [ bib \| DOI \| .pdf ]
[103]	N. A. Barnafi, L. M. De Oliveira Vilaca, M. C. Milinkovitch, and R. Ruiz-Baier Coupling chemotaxis and growth poromechanics for the modelling of feather primordia patterning. Mathematics, 10:e4096(1–25), 2022. [ bib \| DOI \| .pdf ]
[102]	N. Barnafi, B. Gómez-Vargas, W. d. J. Lourenço, R. F. Reis, B. M. Rocha, M. Lobosco, R. Ruiz-Baier, and R. Weber dos Santos Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema. Journal of Scientific Computing, 92:e92(1–40), 2022. [ bib \| DOI \| .pdf ]
[101]	W. M. Boon, M. Hornkjøl, M. Kuchta, K.-A. Mardal, and R. Ruiz-Baier Parameter-robust methods for the Biot–Stokes interfacial coupling without Lagrange multipliers. Journal of Computational Physics, 467:e111464(1–25), 2022. [ bib \| DOI \| .pdf ]
[100]	G. N. Gatica, C. Inzunza, R. Ruiz-Baier, and F. Sandoval A posteriori error analysis of Banach spaces-based fully-mixed finite element methods for Boussinesq-type models. Journal of Numerical Mathematics, 30(4):1–32, 2022. [ bib \| DOI \| .pdf ]
[99]	G. N. Gatica, B. Gómez-Vargas, and R. Ruiz-Baier A posteriori error analysis of mixed finite element methods for stress-assisted diffusion problems. Journal of Computational and Applied Mathematics, 409:e114144(1–23), 2022. [ bib \| DOI \| .pdf ]
[98]	G. N. Gatica, S. Meddahi, and R. Ruiz-Baier An L^p spaces-based formulation yielding a new fully mixed finite element method for the coupled Darcy and heat equations. IMA Journal of Numerical Analysis, 42(4):3154–3206, 2022. [ bib \| DOI \| .pdf ]
[97]	K. Kaouri, N. Christodoulou, A. Chakraborty, P. E. Méndez, P. A. Skourides, and R. Ruiz-Baier A new mechanochemical model for apical constriction: coupling calcium dynamics and viscoelasticity. Frontiers in Systems Biology, 2:e952790(1–13), 2022. [ bib \| DOI \| .pdf ]
[96]	K. Kaouri, P. E. Méndez, and R. Ruiz-Baier Mechanochemical models for calcium waves in embryonic epithelia. Vietnam Journal of Mathematics, 50:947–975, 2022. [ bib \| DOI \| .pdf ]
[95]	W. d. J. Lourenço, R. F. Reis, R. Ruiz-Baier, B. M. Rocha, R. Weber dos Santos, and M. Lobosco A poroelastic approach for modelling myocardial oedema in acute myocarditis. Frontiers in Physiology, 13:e888515(1–14), 2022. [ bib \| DOI \| .pdf ]
[94]	S. Meddahi and R. Ruiz-Baier A new DG method for a pure–stress formulation of the Brinkman problem with strong symmetry. Networks and Heterogeneous Media, 17(6):893–916, 2022. [ bib \| DOI \| .pdf ]
[93]	R. Ruiz-Baier, M. Taffetani, H. D. Westermeyer, and I. Yotov The Biot–Stokes coupling using total pressure: formulation, analysis and application to interfacial flow in the eye. Computer Methods in Applied Mechanics and Engineering, 389:e114384(1–30), 2022. [ bib \| DOI \| .pdf ]
[92]	N. Verma, B. Gómez-Vargas, L. M. De Oliveira Vilaca, S. Kumar, and R. Ruiz-Baier Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media. Applicable Analysis, 101(14):4914–4941, 2022. [ bib \| DOI \| .pdf ]
[91]	M. Álvarez, G. N. Gatica, and R. Ruiz-Baier A mixed-primal finite element method for the coupling of Brinkman-Darcy flow and nonlinear transport. IMA Journal of Numerical Analysis, 41(1):381–411, 2021. [ bib \| DOI \| .pdf ]
[90]	V. Anaya, R. Caraballo, B. Gómez-Vargas, D. Mora, and R. Ruiz-Baier Velocity-vorticity-pressure formulation for the Oseen problem with variable viscosity. Calcolo, 58(4):e44(1–25), 2021. [ bib \| DOI \| .pdf ]
[89]	G. Baird, R. Bürger, P. E. Méndez, and R. Ruiz-Baier Second-order schemes for axisymmetric Navier-Stokes-Brinkman and transport equations modelling water filters. Numerische Mathematik, 147(2):431–479, 2021. [ bib \| DOI \| .pdf ]
[88]	N. Barnafi, G. N. Gatica, D. E. Hurtado, W. Miranda, and R. Ruiz-Baier Adaptive mesh refinement in deformable image registration: A posteriori error estimates for primal and mixed formulations. SIAM Journal on Imaging Sciences, 14(3):1238–1272, 2021. [ bib \| DOI \| .pdf ]
[87]	N. Barnafi, G. N. Gatica, D. E. Hurtado, W. Miranda, and R. Ruiz-Baier New primal and dual-mixed finite element methods for stable image registration with singular regularization. Mathematical Models and Methods in Applied Sciences, 31(5):979–1020, 2021. [ bib \| DOI \| .pdf ]
[86]	W. M. Boon, M. Kuchta, K.-A. Mardal, and R. Ruiz-Baier Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot's equations utilizing total pressure. SIAM Journal on Scientific Computing, 43(4):B961–B983, 2021. [ bib \| DOI \| .pdf ]
[85]	R. Bürger, S. Kumar, D. Mora, R. Ruiz-Baier, and N. Verma Virtual element methods for the three-field formulation of time-dependent linear poroelasticity. Advances in Computational Mathematics, 47:e2(1–37), 2021. [ bib \| DOI \| .pdf ]
[84]	P. E. Farrell, L. F. Gatica, B. P. Lamichhane, R. Oyarzúa, and R. Ruiz-Baier Mixed Kirchhoff stress - displacement - pressure formulations for incompressible hyperelasticity. Computer Methods in Applied Mechanics and Engineering, 374:e113562(1–24), 2021. [ bib \| DOI \| .pdf ]
[83]	G. N. Gatica, R. Oyarzúa, R. Ruiz-Baier, and Y. D. Sobral Banach spaces-based analysis of a fully-mixed finite element method for the steady-state model of fluidized beds. Computers & Mathematics with Applications, 84:244–276, 2021. [ bib \| DOI \| .pdf ]
[82]	A. Khan, M. T. Mohan, and R. Ruiz-Baier Conforming, nonconforming and DG methods for the stationary generalized Burgers-Huxley equation. Journal of Scientific Computing, 88:e52(1–26), 2021. [ bib \| DOI \| .pdf ]
[81]	M. Taffetani, R. Ruiz-Baier, and S. L. Waters Coupling Stokes flow with inhomogeneous poroelasticity. Quarterly Journal of Mechanics and Applied Mathematics, 74(4):411–439, 2021. [ bib \| DOI \| .pdf ]
[80]	J. Almonacid, G. N. Gatica, R. Oyarzúa, and R. Ruiz-Baier A new mixed finite element method for the n-dimensional Boussinesq problem with temperature-dependent viscosity. Networks and Heterogeneous Media, 15(2):215–245, 2020. [ bib \| DOI \| .pdf ]
[79]	J. Almonacid, G. N. Gatica, and R. Ruiz-Baier Ultra-weak symmetry of stress for augmented mixed finite element formulations in continuum mechanics. Calcolo, 57:e2(1–25), 2020. [ bib \| DOI \| .pdf ]
[78]	V. Anaya, Z. De Wijn, B. Gómez-Vargas, D. Mora, and R. Ruiz-Baier Rotation-based mixed formulations for an elasticity-poroelasticity interface problem. SIAM Journal on Scientific Computing, 42(1):B225–B249, 2020. [ bib \| DOI \| .pdf ]
[77]	R. Bürger, P. E. Méndez, and R. Ruiz-Baier Convergence of H(div)-conforming schemes for a new model of sedimentation in circular clarifiers with a rotating rake. Computer Methods in Applied Mechanics and Engineering, 367:e113130(1–24), 2020. [ bib \| DOI \| .pdf ]
[76]	E. Colmenares, G. N. Gatica, S. Moraga, and R. Ruiz-Baier A fully-mixed finite element method for the steady-state Oberbeck-Boussinesq system. The SMAI Journal of Computational Mathematics, 6:125–157, 2020. [ bib \| DOI \| .pdf ]
[75]	L. M. De Oliveira Vilaca, B. Gómez-Vargas, S. Kumar, R. Ruiz-Baier, and N. Verma Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue. Applied Mathematical Modelling, 84:425–446, 2020. [ bib \| DOI \| .pdf ]
[74]	S. Kumar, R. Oyarzúa, R. Ruiz-Baier, and R. Sandilya Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity. ESAIM: Mathematical Modelling and Numerical Analysis, 54(1):273–299, 2020. [ bib \| DOI \| .pdf ]
[73]	F. Levrero-Florencio, F. Margara, E. Zacur, A. Bueno-Orovio, Z. J. Wang, A. Santiago, J. Aguado-Sierra, G. Houzeaux, V. Grau, D. Kay, M. Vázquez, R. Ruiz-Baier, and B. Rodriguez Sensitivity analysis of a strongly-coupled human-based electromechanical cardiac model: effect of mechanical parameters on physiologically relevant biomarkers. Computer Methods in Applied Mechanics and Engineering, 361:e112762(1–31), 2020. [ bib \| DOI \| .pdf ]
[72]	A. Propp, A. Gizzi, F. Levrero-Florencio, and R. Ruiz-Baier An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion. Biomechanics and Modeling in Mechanobiology, 19(2):633–659, 2020. [ bib \| DOI \| .pdf ]
[71]	R. Ruiz-Baier, A. Gizzi, A. Loppini, C. Cherubini, and S. Filippi Modelling thermo-electro-mechanical effects in orthotropic cardiac tissue. Communications in Computational Physics, 27(1):87–115, 2020. [ bib \| DOI \| .pdf ]
[70]	M. Álvarez, G. N. Gatica, B. Gómez-Vargas, and R. Ruiz-Baier New mixed finite element methods for natural convection with phase-change in porous media. Journal of Scientific Computing, 80(1):141–174, 2019. [ bib \| DOI \| .pdf ]
[69]	V. Anaya, A. Bouharguane, D. Mora, C. Reales, R. Ruiz-Baier, N. Seloula, and H. Torres Analysis and approximation of a vorticity-velocity-pressure formulation for the Oseen equations. Journal of Scientific Computing, 80(3):1577–1606, 2019. [ bib \| DOI \| .pdf ]
[68]	V. Anaya, Z. De Wijn, D. Mora, and R. Ruiz-Baier Mixed displacement-rotation-pressure formulations for linear elasticity. Computer Methods in Applied Mechanics and Engineering, 344:71–94, 2019. [ bib \| DOI \| .pdf ]
[67]	V. Anaya, B. Gómez-Vargas, D. Mora, and R. Ruiz-Baier Incorporating variable viscosity in vorticity-based formulations for Brinkman equations. Comptes Rendus Mathématiques, 357(6):552–560, 2019. [ bib \| DOI \| .pdf ]
[66]	V. Anaya, D. Mora, C. Reales, and R. Ruiz-Baier A vorticity-pressure finite element formulation for the Brinkman-Darcy coupled problem. Numerical Methods for Partial Differential Equations, 35(2):528–544, 2019. [ bib \| DOI \| .pdf ]
[65]	R. Bürger, P. E. Méndez, and R. Ruiz-Baier On H(div)-conforming methods for double-diffusion equations in porous media. SIAM Journal on Numerical Analysis, 57(3):1318–1343, 2019. [ bib \| DOI \| .pdf ]
[64]	L. M. De Oliveira Vilaca, M. C. Milinkovitch, and R. Ruiz-Baier Numerical approximation of a 3D mechanochemical interface model for skin patterning. Journal of Computational Physics, 384:383–404, 2019. [ bib \| DOI \| .pdf ]
[63]	G. N. Gatica, B. Gómez-Vargas, and R. Ruiz-Baier Formulation and analysis of fully-mixed finite element methods for stress-assisted diffusion problems. Computers & Mathematics with Applications, 77(5):1312–1330, 2019. [ bib \| DOI \| .pdf ]
[62]	S. Kumar, R. Ruiz-Baier, and R. Sandilya Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems. Journal of Scientific Computing, 78(1):74–93, 2019. [ bib \| DOI \| .pdf ]
[61]	J. Woodfield, M. Álvarez, B. Gómez-Vargas, and R. Ruiz-Baier Stability and finite element approximation of phase change models for natural convection in porous media. Journal of Computational and Applied Mathematics, 360:117–137, 2019. [ bib \| DOI \| .pdf ]
[60]	M. Álvarez, G. N. Gatica, and R. Ruiz-Baier A posteriori error estimation for an augmented mixed-primal method applied to sedimentation-consolidation systems. Journal of Computational Physics, 367:332–346, 2018. [ bib \| DOI \| .pdf ]
[59]	V. Anaya, M. Bendahmane, D. Mora, and R. Ruiz-Baier On a vorticity-based formulation for reaction-diffusion-Brinkman systems. Networks and Heterogeneous Media, 13(1):69–94, 2018. [ bib \| DOI \| .pdf ]
[58]	R. Bürger, S. Kumar Kenettinkara, R. Ruiz-Baier, and H. Torres Coupling of discontinuous Galerkin schemes for viscous flow in porous media with adsorption. SIAM Journal on Scientific Computing, 40(2):B637–B662, 2018. [ bib \| DOI \| .pdf ]
[57]	J. Camaño, R. Oyarzúa, R. Ruiz-Baier, and G. Tierra Error analysis of an augmented mixed method for the Navier-Stokes problem with mixed boundary conditions. IMA Journal of Numerical Analysis, 38(3):1452–1484, 2018. [ bib \| DOI \| .pdf ]
[56]	G. N. Gatica, B. Gómez-Vargas, and R. Ruiz-Baier Analysis and mixed-primal finite element discretisations for stress-assisted diffusion problems. Computer Methods in Applied Mechanics and Engineering, 337:411–438, 2018. [ bib \| DOI \| .pdf ]
[55]	S. Kumar, R. Ruiz-Baier, and R. Sandilya Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media. Computers & Mathematics with Applications, 76(4):923–937, 2018. [ bib \| DOI \| .pdf ]
[54]	A. Loppini, A. Gizzi, R. Ruiz-Baier, C. Cherubini, F. H. Fenton, and S. Filippi Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics. Frontiers in Physiology, 9:e1714(1–16), 2018. [ bib \| DOI \| .pdf ]
[53]	M. Álvarez, G. N. Gatica, and R. Ruiz-Baier A posteriori error analysis of a fully-mixed formulation for the Brinkman-Darcy problem. Calcolo, 54(4):1491–1519, 2017. [ bib \| DOI \| .pdf ]
[52]	V. Anaya, D. Mora, C. Reales, and R. Ruiz-Baier Mixed methods for a stream-function–vorticity formulation of the axisymmetric Brinkman equations. Journal of Scientific Computing, 71(1):348–364, 2017. [ bib \| DOI \| .pdf ]
[51]	V. Anaya, D. Mora, and R. Ruiz-Baier Pure vorticity formulation and Galerkin discretization for the Brinkman equations. IMA Journal of Numerical Analysis, 37(4):2020–2041, 2017. [ bib \| DOI \| http ]
[50]	R. Bürger, R. Ruiz-Baier, and C. Tian Stability analysis and finite volume element discretization for delay-driven spatio-temporal patterns in a predator-prey model. Mathematics and Computers in Simulation, 132:28–52, 2017. [ bib \| DOI \| .pdf ]
[49]	J. Camaño, R. Oyarzúa, G. N. Gatica, and R. Ruiz-Baier An augmented stress-based mixed finite element method for the steady state Navier-Stokes equations with nonlinear viscosity. Numerical Methods for Partial Differential Equations, 33(5):1692–1725, 2017. [ bib \| DOI \| .pdf ]
[48]	C. Cherubini, S. Filippi, A. Gizzi, and R. Ruiz-Baier A note on stress-driven anisotropic diffusion and its role in active deformable media. Journal of Theoretical Biology, 430(7):221–228, 2017. [ bib \| DOI \| .pdf ]
[47]	A. Gizzi, A. Loppini, R. Ruiz-Baier, A. Ippolito, A. Camassa, A. La Camera, E. Emmi, L. Di Perna, V. Garofalo, C. Cherubini, and S. Filippi Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential. Chaos, 27:e093919(1–11), 2017. [ bib \| DOI \| .pdf ]
[46]	P. Lenarda, M. Paggi, and R. Ruiz-Baier Partitioned coupling of advection-diffusion-reaction systems and Brinkman flows. Journal of Computational Physics, 344:281–302, 2017. [ bib \| DOI \| .pdf ]
[45]	A. Quarteroni, T. Lassila, S. Rossi, and R. Ruiz-Baier Integrated Heart – Coupled multiscale and multiphysics models for the simulation of the cardiac function. Computer Methods in Applied Mechanics and Engineering, 314:345–407, 2017. [ bib \| DOI \| .pdf ]
[44]	M. Álvarez, G. N. Gatica, and R. Ruiz-Baier A vorticity-based fully-mixed formulation for the 3D Brinkman-Darcy problem. Computer Methods in Applied Mechanics and Engineering, 307:68–95, 2016. [ bib \| DOI \| .pdf ]
[43]	M. Álvarez, G. N. Gatica, and R. Ruiz-Baier A posteriori error analysis for a viscous flow – transport problem. ESAIM: Mathematical Modelling and Numerical Analysis, 50(6):1789–1816, 2016. [ bib \| DOI \| .pdf ]
[42]	M. Álvarez, G. N. Gatica, and R. Ruiz-Baier Mixed-primal finite element approximation of a steady sedimentation-consolidation system. Mathematical Models and Methods in Applied Sciences, 26(5):867–900, 2016. [ bib \| DOI \| .pdf ]
[41]	V. Anaya, D. Mora, R. Oyarzúa, and R. Ruiz-Baier A priori and a posteriori error analysis of a mixed scheme for the Brinkman problem. Numerische Mathematik, 133(4):781–817, 2016. [ bib \| DOI \| .pdf ]
[40]	M. Bendahmane, R. Ruiz-Baier, and C. Tian Turing pattern dynamics and adaptive discretization of a superdiffusive Lotka-Volterra system. Journal of Mathematical Biology, 72:1441–1465, 2016. [ bib \| DOI \| .pdf ]
[39]	R. Bürger, S. Kumar, S. Kumar Kenettinkara, and R. Ruiz-Baier Discontinuous approximation of viscous two-phase flow in heterogeneous porous media. Journal of Computational Physics, 321:126–150, 2016. [ bib \| DOI \| .pdf ]
[38]	G. N. Gatica, R. Ruiz-Baier, and G. Tierra A mixed finite element method for the Darcy equations with pressure-dependent porosity. Mathematics of Computation, 85(297):1–33, 2016. [ bib \| DOI \| .pdf ]
[37]	G. N. Gatica, R. Ruiz-Baier, and G. Tierra A posteriori error analysis of an augmented mixed method for the Navier-Stokes equations with nonlinear viscosity. Computers & Mathematics with Applications, 72(9):2289–2310, 2016. [ bib \| DOI \| .pdf ]
[36]	R. Oyarzúa and R. Ruiz-Baier Locking-free finite element methods for poroelasticity. SIAM Journal on Numerical Analysis, 54(5):2951–2973, 2016. [ bib \| DOI \| .pdf ]
[35]	R. Ruiz-Baier and I. Lunati Mixed finite element – discontinuous finite volume element discretization of a general class of multicontinuum models. Journal of Computational Physics, 322:666–688, 2016. [ bib \| DOI \| .pdf ]
[34]	M. Álvarez, G. N. Gatica, and R. Ruiz-Baier An augmented mixed–primal finite element method for a coupled flow–transport problem. ESAIM: Mathematical Modelling and Numerical Analysis, 49(5):1399–1427, 2015. [ bib \| DOI \| .pdf ]
[33]	V. Anaya, G. N. Gatica, D. Mora, and R. Ruiz-Baier An augmented velocity-vorticity-pressure formulation for the Brinkman equations. International Journal for Numerical Methods in Fluids, 79(3):109–137, 2015. [ bib \| DOI \| .pdf ]
[32]	V. Anaya, D. Mora, C. Reales, and R. Ruiz-Baier Stabilized mixed approximation of axisymmetric Brinkman flows. ESAIM: Mathematical Modelling and Numerical Analysis, 49(3):855–874, 2015. [ bib \| DOI \| .pdf ]
[31]	B. Andreianov, M. Bendahmane, A. Quarteroni, and R. Ruiz-Baier Solvability analysis and numerical approximation of linearized cardiac electromechanics. Mathematical Models and Methods in Applied Sciences, 25(05):959–993, 2015. [ bib \| DOI \| .pdf ]
[30]	R. Bürger, S. Kumar, and R. Ruiz-Baier Discontinuous finite volume element discretization for coupled flow–transport problems arising in models of sedimentation. Journal of Computational Physics, 299:446–471, 2015. [ bib \| DOI \| .pdf ]
[29]	J. Camaño, R. Oyarzúa, G. N. Gatica, R. Ruiz-Baier, and P. Venegas New fully-mixed finite element methods for the Stokes-Darcy coupling. Computer Methods in Applied Mechanics and Engineering, 295:362–395, 2015. [ bib \| DOI \| .pdf ]
[28]	M. Dupraz, S. Filippi, A. Gizzi, A. Quarteroni, and R. Ruiz-Baier Finite element and finite volume-element simulation of pseudo-ECGs and cardiac alternans. Mathematical Methods in the Applied Sciences, 38(6):1046–1058, 2015. [ bib \| DOI \| .pdf ]
[27]	S. Kumar and R. Ruiz-Baier Equal order discontinuous finite volume element methods for the Stokes problem. Journal of Scientific Computing, 65(3):956–978, 2015. [ bib \| DOI \| .pdf ]
[26]	R. Ruiz-Baier Primal-mixed formulations for reaction-diffusion systems on deforming domains. Journal of Computational Physics, 299:320–338, 2015. [ bib \| DOI \| .pdf ]
[25]	R. Ruiz-Baier and H. Torres Numerical solution of a multidimensional sedimentation problem using finite volume-element methods. Applied Numerical Mathematics, 95:280–291, 2015. [ bib \| DOI \| .pdf ]
[24]	Z. Lin, R. Ruiz-Baier, and C. Tian Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion. Journal of Computational Physics, 256:806–823, 2014. [ bib \| DOI \| .pdf ]
[23]	S. Rossi, T. Lassila, R. Ruiz-Baier, A. Sequeira, and A. Quarteroni Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics. European Journal of Mechanics: A/Solids, 48:129–142, 2014. [ bib \| DOI \| .pdf ]
[22]	R. Ruiz-Baier, A. Gizzi, S. Rossi, C. Cherubini, A. Laadhari, S. Filippi, and A. Quarteroni Mathematical modeling of active contraction in isolated cardiomyocytes. Mathematical Medicine and Biology, 31(3):259–283, 2014. [ bib \| DOI \| .pdf ]
[21]	V. Anaya, D. Mora, and R. Ruiz-Baier An augmented mixed finite element method for the vorticity-velocity-pressure formulation of the Stokes equations. Computer Methods in Applied Mechanics and Engineering, 267:261–274, 2013. [ bib \| DOI \| .pdf ]
[20]	D. Baroli, A. Quarteroni, and R. Ruiz-Baier Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity. Advances in Computational Mathematics, 39(2):425–443, 2013. [ bib \| DOI \| .pdf ]
[19]	A. Laadhari, R. Ruiz-Baier, and A. Quarteroni Fully Eulerian finite element approximation of a fluid-structure interaction problem in cardiac cells. International Journal for Numerical Methods in Engineering, 96(11):712–738, 2013. [ bib \| DOI \| .pdf ]
[18]	R. Ruiz-Baier and C. Tian Mathematical analysis and numerical simulation of pattern formation under cross-diffusion. Nonlinear Analysis: Real World Applications, 14(1):601–612, 2013. [ bib \| DOI \| .pdf ]
[17]	B. Ainseba, M. Bendahmane, and R. Ruiz-Baier Analysis of an optimal control problem for the tridomain model in cardiac electrophysiology. Journal of Mathematical Analysis and Applications, 388(1):231–247, 2012. [ bib \| DOI \| .pdf ]
[16]	R. Bürger, R. Ruiz-Baier, K. Schneider, and H. Torres A multiresolution method for the simulation of sedimentation in inclined channels. International Journal of Numerical Analysis & Modeling, 9(3):479–504, 2012. [ bib \| DOI \| .pdf ]
[15]	R. Bürger, R. Ruiz-Baier, and H. Torres A stabilized finite volume element formulation for sedimentation-consolidation processes. SIAM Journal on Scientific Computing, 34(3):B265–B289, 2012. [ bib \| DOI \| .pdf ]
[14]	F. Nobile, A. Quarteroni, and R. Ruiz-Baier An active strain electromechanical model for cardiac tissue. International Journal for Numerical Methods in Biomedical Engineering, 28(1):52–71, 2012. [ bib \| DOI \| .pdf ]
[13]	S. Rossi, R. Ruiz-Baier, L. F. Pavarino, and A. Quarteroni Orthotropic active strain models for the numerical simulation of cardiac biomechanics. International Journal for Numerical Methods in Biomedical Engineering, 28(6–7):761–788, 2012. [ bib \| DOI \| .pdf ]
[12]	B. Andreianov, M. Bendahmane, and R. Ruiz-Baier Analysis of a finite volume method for a cross-diffusion model in population dynamics. Mathematical Models and Methods in Applied Sciences, 21(02):307–344, 2011. [ bib \| DOI \| .pdf ]
[11]	S. Berres and R. Ruiz-Baier A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion. Nonlinear Analysis: Real World Applications, 12(5):2888–2903, 2011. [ bib \| DOI \| .pdf ]
[10]	S. Berres, R. Ruiz-Baier, H. Schwandt, and E. M. Tory An adaptive finite-volume method for a model of two-phase pedestrian flow. Networks and Heterogeneous Media, 6(3):401–423, 2011. [ bib \| DOI \| .pdf ]
[9]	A. Quarteroni and R. Ruiz-Baier Analysis of a finite volume element method for the Stokes problem. Numerische Mathematik, 118(4):737–764, 2011. [ bib \| DOI \| .pdf ]
[8]	M. Bendahmane, R. Bürger, and R. Ruiz-Baier A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology. Numerical Methods for Partial Differential Equations, 26(6):1377–1404, 2010. [ bib \| DOI \| .pdf ]
[7]	M. Bendahmane, R. Bürger, and R. Ruiz-Baier A finite volume scheme for cardiac propagation in media with isotropic conductivities. Mathematics and Computers in Simulation, 80(9):1821–1840, 2010. [ bib \| DOI \| .pdf ]
[6]	R. Bürger, R. Ruiz-Baier, and K. Schneider Adaptive multiresolution methods for the simulation of waves in excitable media. Journal of Scientific Computing, 43(2):261–290, 2010. [ bib \| DOI \| .pdf ]
[5]	M. Bendahmane, R. Bürger, R. Ruiz-Baier, and K. Schneider Adaptive multiresolution schemes with local time stepping for two-dimensional degenerate reaction-diffusion systems. Applied Numerical Mathematics, 59(7):1668–1692, 2009. [ bib \| DOI \| .pdf ]
[4]	M. Bendahmane, R. Bürger, R. Ruiz-Baier, and J. M. Urbano On a doubly nonlinear diffusion model of chemotaxis with prevention of overcrowding. Mathematical Methods in the Applied Sciences, 32(13):1704–1737, 2009. [ bib \| DOI \| .pdf ]
[3]	R. Bürger and R. Ruiz-Baier Multiresolution simulation of reaction-diffusion systems with strong degeneracy. SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, 47:73–80, 2009. [ bib \| DOI \| .pdf ]
[2]	R. Bürger, R. Ruiz, K. Schneider, and M. Sepúlveda Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension. ESAIM: Mathematical Modelling and Numerical Analysis, 42(4):535–563, 2008. [ bib \| DOI \| .pdf ]
[1]	R. Bürger, R. Ruiz, K. Schneider, and M. Sepúlveda Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux. Journal of Engineering Mathematics, 60(3-4):365–385, 2008. [ bib \| DOI \| .pdf ]

Conference proceedings and book chapters

[21]	A. F. AlSohaim, R. Ruiz-Baier, and S. Villa-Fuentes Analysis of a finite element method for the Stokes–Poisson–Boltzmann equations. 2025. [ bib \| DOI \| arXiv \| .pdf ]
[20]	I. U. Ahmed, J. A. Flegg, C. Miller, R. Ruiz-Baier, J. Won, and A. Zanca Multiphase Models for Moving Boundary Problems in Biology. In D. R. Wood, J. de Gier, and C. E. Praeger, editors, 2021-2022 MATRIX Annals, pages 289–307. Springer Nature Switzerland, Cham, 2024. [ bib \| DOI \| .pdf ]
[19]	R. Bürger, A. Khan, P. E. Méndez, and R. Ruiz-Baier A divergence-conforming method for flow and double-diffusive transport. Proceedings in Applied Mathematics and Mechanics, 24:e202400201, 2024. [ bib \| DOI \| .pdf ]
[18]	W. M. Boon, M. Hornkjøl, M. Kuchta, K.-A. Mardal, R. Ruiz-Baier, M. Taffetani, H. D. Westermeyer, and I. Yotov Mixed formulations for poroelasticity/free-flow using total pressure. In M. Peszynska, S. Pop, B. Wohlmuth, and Z. Yosibash, editors, Multiscale Coupled Models for Complex Media: From Analysis to Simulation in Geophysics and Medicine, Oberwolfach Reports, pages 33–35. Mathematisches Forschungsinstitut Oberwolfach, Germany, 2022. [ bib \| DOI \| .pdf ]
[17]	M. Álvarez, B. Gómez-Vargas, R. Ruiz-Baier, and J. Woodfield Stability of a second-order method for phase change in porous media flow. Proceedings in Applied Mathematics and Mechanics, 18(1):e201800021–2, 2018. [ bib \| DOI \| .pdf ]
[16]	R. Bürger, J. Careaga, S. Diehl, C. Mejías, and R. Ruiz-Baier Convection-diffusion-reaction and transport-flow problems motivated by models of sedimentation: some recent advances. In B. Sirakov, P. de Souza, and M. Viana, editors, Proceedings of the International Congress of Mathematicians, volume IV: Invited Lectures, pages 3489–3514. World Scientific, Singapore, 2018. [ bib \| DOI \| .pdf ]
[15]	R. Bürger, S. Kumar Kenettinkara, R. Ruiz-Baier, and H. Torres Discontinuous approximation of flow in porous media with adsorption. Proceedings in Applied Mathematics and Mechanics, 18(1):e201800064–5, 2018. [ bib \| DOI \| .pdf ]
[14]	A. Gizzi, A. Propp, and R. Ruiz-Baier Mixed formulations for stress-assisted diffusion problems in cardiac biomechanics. In M. Mallayya, editor, ICNumACA'18: Proceedings of the International Conference on Numerical Analysis, Computing and Applications, volume 1, pages 1–18. Mohandas College of Engineering, Kerala - India, 2018. [ bib \| DOI \| .pdf ]
[13]	S. Kumar, R. Ruiz-Baier, and R. Sandilya Discontinuous finite volume element methods for the optimal control of Brinkman equations. In C. Cancès and P. Omnes, editors, Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, volume 200 of Springer Proc. Math. Stat., pages 307–315. Springer International Publishing, 2017. [ bib \| DOI \| .pdf ]
[12]	R. Bürger, S. Kumar, S. Kumar Kenettinkara, and R. Ruiz-Baier A discontinuous method for oil-water flow in heterogeneous porous media. Proceedings in Applied Mathematics and Mechanics, 16:763–764, 2016. [ bib \| DOI \| .pdf ]
[11]	A. Gizzi, R. Ruiz-Baier, S. Rossi, A. Laadhari, C. Cherubini, and S. Filippi A three-dimensional continuum model of active contraction in single cardiomyocytes. In A. Quarteroni, editor, Modeling the Heart and the Circulatory System, pages 157–176. Springer-Verlag, Milano, 2015. [ bib \| DOI \| .pdf ]
[10]	F. Betancourt, R. Bürger, R. Ruiz-Baier, H. Torres, and C. A. Vega On numerical methods for hyperbolic conservation laws and related equations modelling sedimentation of solid-liquid suspensions. In G.-Q. G. Chen, H. Holden, and K. H. Karlsen, editors, Hyperbolic conservation laws and related analysis with applications, volume 49 of Springer Proc. Math. Stat., pages 23–68. Springer, Heidelberg, 2014. [ bib \| DOI \| .pdf ]
[9]	R. Ruiz-Baier, D. Ambrosi, S. Pezzuto, S. Rossi, and A. Quarteroni Activation models for the numerical simulation of cardiac electromechanical interactions. In G. Holzapfel and E. Kuhl, editors, Computer Models in Biomechanics: From Nano to Macro, pages 189–201. Springer, Netherlands, 2013. [ bib \| DOI \| .pdf ]
[8]	S. Berres and R. Ruiz-Baier Simulation of an epidemic model with nonlinear cross-diffusion. In E. Vázquez-Cendón, A. Hidalgo, P. García-Navarro, and L. Cea, editors, Numerical Methods for Hyperbolic Equations, pages 331–338. CRC Press/Balkema, Leiden, 2012. [ bib \| DOI \| .pdf ]
[7]	S. Berres, R. Ruiz-Baier, H. Schwandt, and E. M. Tory A two-dimensional model of pedestrian flow generating pattern formation. In T. Li and S. Jiang, editors, Hyperbolic problems–theory, numerics and applications. Volume 1, volume 17–18 of Ser. Contemp. Appl. Math. CAM, pages 304–311. World Sci. Publishing, Singapore, 2012. [ bib \| DOI ]
[6]	R. Bürger, R. Ruiz-Baier, and H. Torres A finite volume element method for simulating secondary settling tanks. Proceedings in Applied Mathematics and Mechanics, 12(1):667–668, 2012. [ bib \| DOI \| .pdf ]
[5]	A. Quarteroni, S. Rossi, and R. Ruiz-Baier On some numerical aspects of an active strain model in cardiac mechanics. In P. Nithiarasu, editor, CMBE11: 2nd International Conference on Computational & Mathematical Biomedical Engineering, volume 1, pages 328–331. Swansea University, UK, 2011. [ bib \| DOI ]
[4]	S. Rossi, R. Ruiz-Baier, L. F. Pavarino, and A. Quarteroni Active strain and activation models in cardiac electromechanics. Proceedings in Applied Mathematics and Mechanics, 11(1):119–120, 2011. [ bib \| DOI \| .pdf ]
[3]	R. Bürger and R. Ruiz-Baier Adaptive multiresolution simulation of waves in electrocardiology. In G. Kreiss, P. Lötstedt, A. Målqvist, and M. Neytcheva, editors, Numerical Mathematics and Advanced Applications, number 2 in Springer Proc. Math. Stat., pages 199–207. Springer, Heidelberg, 2010. [ bib \| DOI \| .pdf ]
[2]	M. Bendahmane, R. Bürger, R. Ruiz-Baier, and K. Schneider Adaptive multiresolution schemes for reaction-diffusion systems. Proceedings in Applied Mathematics and Mechanics, 8(1):10969–10970, 2008. [ bib \| DOI \| .pdf ]
[1]	R. Bürger, R. Ruiz, K. Schneider, and M. Sepúlveda Multiresolution schemes for an extended clarifier-thickener model. Proceedings in Applied Mathematics and Mechanics, 7(1):1041803–1041804, 2007. [ bib \| DOI \| .pdf ]

Theses

[2]	R. Ruiz-Baier Numerical Methods and Analysis of Degenerate Parabolic Equations and Reaction-Diffusion Systems. PhD thesis in Applied Sciences with mention in Mathematical Engineering, Universidad de Concepción, Chile, December 2008. [ bib \| http \| .pdf ]
[1]	R. Ruiz-Baier Métodos de Multiresolución y su Aplicación a un Modelo de Ingeniería. Mathematical Engineering thesis, Universidad de Concepción, Chile, March 2005. [ bib \| http \| .pdf ]

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