Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system

Nicolas Besse; Dietmar Kröner

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 6, page 1177-1202
  • ISSN: 0764-583X

Abstract

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We present the convergence analysis of locally divergence-free discontinuous Galerkin methods for the induction equations which appear in the ideal magnetohydrodynamic system. When we use a second order Runge Kutta time discretization, under the CFL condition Δ t ∼ h 4 / 3 , we obtain error estimates in L2 of order 𝒪 ( Δ t 2 + h m + 1 / 2 ) where m is the degree of the local polynomials.

How to cite

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Besse, Nicolas, and Kröner, Dietmar. "Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system." ESAIM: Mathematical Modelling and Numerical Analysis 39.6 (2010): 1177-1202. <http://eudml.org/doc/194301>.

@article{Besse2010,
abstract = { We present the convergence analysis of locally divergence-free discontinuous Galerkin methods for the induction equations which appear in the ideal magnetohydrodynamic system. When we use a second order Runge Kutta time discretization, under the CFL condition $\Delta t\sim h^\{4/3\}$, we obtain error estimates in L2 of order $\mathcal\{O\} (\Delta t^2 + h^\{m + 1/2\})$ where m is the degree of the local polynomials. },
author = {Besse, Nicolas, Kröner, Dietmar},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Magnetohydrodynamics; discontinuous-Galerkin methods; convergence analysis.; second-order Runge Kutta time discretization; CFL condition},
language = {eng},
month = {3},
number = {6},
pages = {1177-1202},
publisher = {EDP Sciences},
title = {Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system},
url = {http://eudml.org/doc/194301},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Besse, Nicolas
AU - Kröner, Dietmar
TI - Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 6
SP - 1177
EP - 1202
AB - We present the convergence analysis of locally divergence-free discontinuous Galerkin methods for the induction equations which appear in the ideal magnetohydrodynamic system. When we use a second order Runge Kutta time discretization, under the CFL condition $\Delta t\sim h^{4/3}$, we obtain error estimates in L2 of order $\mathcal{O} (\Delta t^2 + h^{m + 1/2})$ where m is the degree of the local polynomials.
LA - eng
KW - Magnetohydrodynamics; discontinuous-Galerkin methods; convergence analysis.; second-order Runge Kutta time discretization; CFL condition
UR - http://eudml.org/doc/194301
ER -

References

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