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

作　　者：Hassan Fahs 

机构地区：[1]IFP,1 & 4 avenue de Bois-Préau,92852 Rueil-Malmaison Cedex,France

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2009年第3期275-300,共26页高等学校计算数学学报（英文版）

基　　金：supported by a grant from the French National Ministry of Education and Research(MENSR,19755-2005)

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 pro- posed method combines a centered approximation for the evaluation of fluxes at the in- terface between neighboring elements, with a Nth-order leap-frog time scheme. More- over, 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 Maxwelrs 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.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.

关 键 词：Maxwell＇s equations discontinuous Galerkin method leap-frog time scheme stability convergence non-conforming meshes high-order accuracy. 

分 类 号：O441.4[理学—电磁学]