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

Hassan Fahs (1)

1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media

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.

Mots clés: Maxwell's equations; discontinuous Galerkin method; non-conforming meshes; high-order accuracy.; leap-frog time scheme; stability; convergence; high-order accuracy

Domaines: Physique mathématique [math-ph]; Electromagnétisme

Hassan Fahs. High-Order Leap-Frog Based Discontinuous Galerkin Method for the Time-Domain Maxwell Equations on Non-Conforming Simplicial Meshes. Numerical Mathematics: Theory, Methods and Applications, 2009, 2 (3), pp.275 - 300. ⟨hal-00600467⟩