The incompressible MHD equations couple Navier-Stokes equations with Maxwell’s equations to describe the flow of a viscous, incompressible, and electrically conducting fluid in a Lipschitz domain . We verify convergence of iterates of different coupling and decoupling fully discrete schemes towards weak solutions for vanishing discretization parameters. Optimal first order of convergence is shown in the presence of strong solutions for a splitting scheme which decouples the computation of velocity field, pressure, and magnetic fields at every iteration step.
Mots-clés : magneto-hydrodynamics, discretization, FEM, fixed-point scheme, splitting-method
@article{M2AN_2008__42_6_1065_0, author = {Prohl, Andreas}, title = {Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {1065--1087}, publisher = {EDP-Sciences}, volume = {42}, number = {6}, year = {2008}, doi = {10.1051/m2an:2008034}, mrnumber = {2473320}, zbl = {1149.76029}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2008034/} }
TY - JOUR AU - Prohl, Andreas TI - Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 1065 EP - 1087 VL - 42 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008034/ DO - 10.1051/m2an:2008034 LA - en ID - M2AN_2008__42_6_1065_0 ER -
%0 Journal Article %A Prohl, Andreas %T Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 1065-1087 %V 42 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008034/ %R 10.1051/m2an:2008034 %G en %F M2AN_2008__42_6_1065_0
Prohl, Andreas. Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 6, pp. 1065-1087. doi : 10.1051/m2an:2008034. http://www.numdam.org/articles/10.1051/m2an:2008034/
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