In this paper we analyze the coupling of a scalar nonlinear convection-diffusion problem with the Stokes equations where the viscosity depends on the distribution of the solution to the transport problem. An augmented variational approach for the fluid flow coupled with a primal formulation for the transport model is proposed. The resulting Galerkin scheme yields an augmented mixed-primal finite element method employing Raviart−Thomas spaces of order
Mots-clés : Stokes equations, nonlinear transport problem, augmented mixed-primal formulation, fixed point theory, thermal convection, sedimentation-consolidation process, finite element methods, a priori error analysis
@article{M2AN_2015__49_5_1399_0, author = {Alvarez, Mario and Gatica, Gabriel N. and Ruiz{\textendash}Baier, Ricardo}, title = {An augmented mixed-primal finite element method for a coupled flow-transport problem}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1399--1427}, publisher = {EDP-Sciences}, volume = {49}, number = {5}, year = {2015}, doi = {10.1051/m2an/2015015}, mrnumber = {3423229}, zbl = {1329.76157}, language = {en}, url = {https://www.numdam.org/articles/10.1051/m2an/2015015/} }
TY - JOUR AU - Alvarez, Mario AU - Gatica, Gabriel N. AU - Ruiz–Baier, Ricardo TI - An augmented mixed-primal finite element method for a coupled flow-transport problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 1399 EP - 1427 VL - 49 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2015015/ DO - 10.1051/m2an/2015015 LA - en ID - M2AN_2015__49_5_1399_0 ER -
%0 Journal Article %A Alvarez, Mario %A Gatica, Gabriel N. %A Ruiz–Baier, Ricardo %T An augmented mixed-primal finite element method for a coupled flow-transport problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 1399-1427 %V 49 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2015015/ %R 10.1051/m2an/2015015 %G en %F M2AN_2015__49_5_1399_0
Alvarez, Mario; Gatica, Gabriel N.; Ruiz–Baier, Ricardo. An augmented mixed-primal finite element method for a coupled flow-transport problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1399-1427. doi : 10.1051/m2an/2015015. https://www.numdam.org/articles/10.1051/m2an/2015015/
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