Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system
ESAIM: Modélisation mathématique et analyse numérique, Volume 39 (2005) no. 6, pp. 1177-1202.

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 Δth 4/3 , we obtain error estimates in L 2 of order 𝒪(Δt 2 +h m+1/2 ) where m is the degree of the local polynomials.

DOI: 10.1051/m2an:2005051
Classification: 76W05, 65J10
Keywords: magnetohydrodynamics, discontinuous-Galerkin methods, convergence analysis
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     author = {Besse, Nicolas and Kr\"oner, Dietmar},
     title = {Convergence of locally divergence-free {discontinuous-Galerkin} methods for the induction equations of the {2D-MHD} system},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {1177--1202},
     publisher = {EDP-Sciences},
     volume = {39},
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Besse, Nicolas; Kröner, Dietmar. Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system. ESAIM: Modélisation mathématique et analyse numérique, Volume 39 (2005) no. 6, pp. 1177-1202. doi : 10.1051/m2an:2005051. http://www.numdam.org/articles/10.1051/m2an:2005051/

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