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A fully‐mixed finite element method for the coupling of the Navier–Stokes and Darcy–Forchheimer equations
Sergio Caucao, Gabriel N. Gatica and Felipe Sandoval Numerical Methods for Partial Differential Equations 37(3) 2550 (2021) https://doi.org/10.1002/num.22745
Further developments on boundary-field equation methods for nonlinear transmission problems
A fully mixed finite element method for the coupling of the Stokes and Darcy–Forchheimer problems
Antonio Márquez, Gabriel N Gatica, Hugo S Díaz and Javier A Almonacid IMA Journal of Numerical Analysis 40(2) 1454 (2020) https://doi.org/10.1093/imanum/dry099
Consistency of a phase field regularisation for an inverse problem governed by a quasilinear Maxwell system
A conforming mixed finite element method for the Navier–Stokes/Darcy–Forchheimer coupled problem
Sergio Caucao, Marco Discacciati, Gabriel N. Gatica and Ricardo Oyarzúa ESAIM: Mathematical Modelling and Numerical Analysis 54(5) 1689 (2020) https://doi.org/10.1051/m2an/2020009
A Mixed Virtual Element Method for Quasi-Newtonian Stokes Flows
Ernesto Cáceres, Gabriel N. Gatica and Filánder A. Sequeira SIAM Journal on Numerical Analysis 56(1) 317 (2018) https://doi.org/10.1137/17M1121160
Lagrange Multipliers and mixed formulations for some inequality constrained variational inequalities and some nonsmooth unilateral problems
A primal-mixed formulation for the strong coupling of quasi-Newtonian fluids with porous media
Sebastián Domínguez, Gabriel N. Gatica, Antonio Márquez and Salim Meddahi Advances in Computational Mathematics 42(3) 675 (2016) https://doi.org/10.1007/s10444-015-9439-7
A stabilized finite element analysis for a power-law pseudoplastic Stokes problem
Analysis of an augmented pseudostress-based mixed formulation for a nonlinear Brinkman model of porous media flow
Gabriel N. Gatica, Luis F. Gatica and Filánder A. Sequeira Computer Methods in Applied Mechanics and Engineering 289 104 (2015) https://doi.org/10.1016/j.cma.2015.01.019
Mixed variational formulations in locally convex spaces
A priori and a posteriori error analyses of a velocity-pseudostress formulation for a class of quasi-Newtonian Stokes flows
Gabriel N. Gatica, Antonio Márquez and Manuel A. Sánchez Computer Methods in Applied Mechanics and Engineering 200(17-20) 1619 (2011) https://doi.org/10.1016/j.cma.2011.01.010
Inf–sup conditions for twofold saddle point problems
Enriched finite element subspaces for dual–dual mixed formulations in fluid mechanics and elasticity
Rommel Bustinza, Gabriel N. Gatica, María González, Salim Meddahi and Ernst P. Stephan Computer Methods in Applied Mechanics and Engineering 194(2-5) 427 (2005) https://doi.org/10.1016/j.cma.2004.02.024
A mixed finite element method for the generalized Stokes problem
Rommel Bustinza, Gabriel N. Gatica and María González International Journal for Numerical Methods in Fluids 49(8) 877 (2005) https://doi.org/10.1002/fld.1029
A Local Discontinuous Galerkin Method for Nonlinear Diffusion Problems with Mixed Boundary Conditions