3D Maxwell's equations and orthogonal nonconforming meshes: a hp-type Discontinuous Galerkin method
Abstract
We present a Discontinuous Galerkin scheme to solve the time-domain Maxwell's equations on conforming or nonconforming orthogonal grids. The method relies on a set of local basis functions whose degree may vary at subgrid interfaces. We also choose a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. We prove that the resulting scheme is stable and that it conserves a discrete analog of the electromagnetic energy. We also analyse the dispersion error in the uniform mesh case.
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