High-order time integration Leap-Frog schemes combined with a discontinuous Galerkin method for the solution of the Maxwell equations
Abstract
In this report, after pedagogical mathematical insight into basic notions of numerical analysis for differential equations, more specific Discontinuous Galerkin (DG) method is introduced. Afterwards, the DG method is combined with a fourth-order staggered Leap-Frog (LF4) scheme to be applied to the solution of the Maxwell equations wave-propagation problem. Stability analysis of the resulting scheme is performed and some peculiarities related with the choice of basis functions in the DG method are stressed.
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