no. 5
Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations
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

DOI : 10.1051/m2an/2012002
Classification : 65M12, 65M60, 78M10
Keywords: temporal convergence, discontinuous Galerkin method, time-domain Maxwell equations, component splitting, order reduction 
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     title = {Temporal convergence of a locally implicit discontinuous {Galerkin} method for {Maxwell's} equations},
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Moya, Ludovic. Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 5, pp. 1225-1246. doi: 10.1051/m2an/2012002

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