Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system

Andreas Prohl

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 6, page 1065-1087
  • ISSN: 0764-583X

Abstract

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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 Ω ⊂ ℝ 3 . 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.

How to cite

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Prohl, Andreas. "Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system." ESAIM: Mathematical Modelling and Numerical Analysis 42.6 (2008): 1065-1087. <http://eudml.org/doc/250280>.

@article{Prohl2008,
abstract = { 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 $\Omega \subset \mathbb\{R\}^3$. 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. },
author = {Prohl, Andreas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Magneto-hydrodynamics; discretization; FEM; fixed-point scheme; splitting-method.; fixed point scheme; splitting method; weak solutions},
language = {eng},
month = {8},
number = {6},
pages = {1065-1087},
publisher = {EDP Sciences},
title = {Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system},
url = {http://eudml.org/doc/250280},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Prohl, Andreas
TI - Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/8//
PB - EDP Sciences
VL - 42
IS - 6
SP - 1065
EP - 1087
AB - 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 $\Omega \subset \mathbb{R}^3$. 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.
LA - eng
KW - Magneto-hydrodynamics; discretization; FEM; fixed-point scheme; splitting-method.; fixed point scheme; splitting method; weak solutions
UR - http://eudml.org/doc/250280
ER -

References

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