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

Besse, Nicolas; Kröner, Dietmar

doi:10.1051/m2an:2005051

Besse, Nicolas ; Kröner, Dietmar

ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 6, pp. 1177-1202

Résumé

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 $Δ t \sim h^{4 / 3}$ , we obtain error estimates in $L^{2}$ of order $𝒪 (Δ t^{2} + h^{m + 1 / 2})$ where $m$ is the degree of the local polynomials.

MR Zbl | 2 citations dans Numdam

DOI : 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: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {1177--1202},
     year = {2005},
     publisher = {EDP Sciences},
     volume = {39},
     number = {6},
     doi = {10.1051/m2an:2005051},
     mrnumber = {2195909},
     zbl = {1084.76046},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an:2005051/}
}

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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, Tome 39 (2005) no. 6, pp. 1177-1202. doi: 10.1051/m2an:2005051

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