A non-conforming discontinuous Galerkin method for solving Maxwell's equations

Hassan Fahs 1
1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : This paper reviews the main features of a high-order non-dissipative discontinuous Galerkin (DG) method recently investigated in [H. Fahs, Int. J. Numer. Anal. Model., 6, 193-216, 2009] for solving Maxwell's equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a fourth-order leap-frog time integration scheme. Moreover, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary-level hanging nodes.
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Hassan Fahs. A non-conforming discontinuous Galerkin method for solving Maxwell's equations. NUMELEC 2008, Dec 2008, Liège, Belgium. 2-p. ⟨hal-00452258⟩

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