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Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system
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- Journal:
- ESAIM: Mathematical Modelling and Numerical Analysis / Volume 39 / Issue 6 / November 2005
- Published online by Cambridge University Press:
- 15 November 2005, pp. 1177-1202
- Print publication:
- November 2005
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- Article
- Export citation
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We present the convergence analysis of locally divergence-free discontinuous Galerkin methodsfor 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 L 2 of order $\mathcal{O} (\Delta t^2 + h^{m + 1/2})$ 
where m is the degree of the local polynomials.
