High-Order Leap-Frog Based Discontinuous Galerkin Method for the Time-Domain Maxwell Equations on Non-Conforming Simplicial Meshes

摘要

A high-order leap-frog based non-dissipative discontinuous Galerkin time-domain method for solving Maxwell's equations is introduced and analyzed.The proposed method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements,with a Nth-order leap-frog time 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.The method is proved to be stable under some CFL-like condition on the time step.The convergence of the semi-discrete approximation to Maxwell's equations is established rigorously and bounds on the global divergence error are provided.Numerical experiments with high-order elements show the potential of the method.