Computational performance of LDG methods applied to time harmonic Maxwell equation in polyhedral domains (Q292542)

The authors provide a numerical study of two versions of the local discontinuous Galerkin (LDG) method applied to time harmonic Maxwell equations on a 3D domain. The methods use numerical fluxes defined as convex combinations of local quantities, which result in a substantial reduction of the stencil. A series of numerical experiments are carried out in 3D polyhedral domains for real and complex valued fields. For unstructured meshes, classical rates of convergence of order \(p+1\) and \(p\) are obtained. On Cartesian meshes, the results suggest superconvergence phenomena and convergence for piecewise constant approximations. The numerical results are compared with computations performed with finite difference and a mode matching method.