Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations

Moya, Ludovic

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 5, pp. 1225-1246.

In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell's equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order reduction

Classification : 65M12, 65M60, 78M10
Mots clés : temporal convergence, discontinuous Galerkin method, time-domain Maxwell equations, component splitting, order reduction

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