A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics

We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P^3_{k}-P_{k-1} elements whereas the magnetic part of the equations is app...

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Main Authors: Houston, Paul, Schoetzau, Dominik, Wei, Xiaoxi
Format: Article
Published: Springer 2008
Online Access:https://eprints.nottingham.ac.uk/912/
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author Houston, Paul
Schoetzau, Dominik
Wei, Xiaoxi
author_facet Houston, Paul
Schoetzau, Dominik
Wei, Xiaoxi
author_sort Houston, Paul
building Nottingham Research Data Repository
collection Online Access
description We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P^3_{k}-P_{k-1} elements whereas the magnetic part of the equations is approximated by discontinuous P^3_{k}-P_{k+1} elements. We carry out a complete a-priori error analysis and prove that the energy norm error is convergent of order O(h^k) in the mesh size h. We also show that the method is able to correctly capture and resolve the strongest magnetic singularities in non-convex polyhedral domains. These results are verified in a series of numerical experiments.
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spelling nottingham-9122020-05-04T20:27:46Z https://eprints.nottingham.ac.uk/912/ A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics Houston, Paul Schoetzau, Dominik Wei, Xiaoxi We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P^3_{k}-P_{k-1} elements whereas the magnetic part of the equations is approximated by discontinuous P^3_{k}-P_{k+1} elements. We carry out a complete a-priori error analysis and prove that the energy norm error is convergent of order O(h^k) in the mesh size h. We also show that the method is able to correctly capture and resolve the strongest magnetic singularities in non-convex polyhedral domains. These results are verified in a series of numerical experiments. Springer 2008 Article NonPeerReviewed Houston, Paul, Schoetzau, Dominik and Wei, Xiaoxi (2008) A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics. Journal of Scientific Computing . (Submitted)
spellingShingle Houston, Paul
Schoetzau, Dominik
Wei, Xiaoxi
A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics
title A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics
title_full A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics
title_fullStr A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics
title_full_unstemmed A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics
title_short A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics
title_sort mixed discontinuous galerkin method for incompressible magnetohydrodynamics
url https://eprints.nottingham.ac.uk/912/