Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 6, p. 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 : https://doi.org/10.1051/m2an:2005051
Classification:  76W05,  65J10
Keywords: magnetohydrodynamics, discontinuous-Galerkin methods, convergence analysis
@article{M2AN_2005__39_6_1177_0,
     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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {6},
     year = {2005},
     pages = {1177-1202},
     doi = {10.1051/m2an:2005051},
     zbl = {1084.76046},
     mrnumber = {2195909},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_6_1177_0}
}
Besse, Nicolas; 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 - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 6, pp. 1177-1202. doi : 10.1051/m2an:2005051. http://www.numdam.org/item/M2AN_2005__39_6_1177_0/

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