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Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system. (English) Zbl 1084.76046
Summary: 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 \(L^2\) of order \({\mathcal O}(\Delta t^2+h^{m+1/2})\), where \(m\) is the degree of the local polynomials

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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