hal-00600467, version 1
High-Order Leap-Frog Based Discontinuous Galerkin Method for the Time-Domain Maxwell Equations on Non-Conforming Simplicial Meshes
Numerical Mathematics: A Journal of Chinese Universities 2, 3 (2009) 275 - 300
Abstract: 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.
- 1:
- CNRS : UMR6621 – INRIA – Université Nice Sophia Antipolis [UNS]
- 2:
- CNRS : UMR6172 – Université de Limoges
- Domain : Mathematics/Mathematical Physics
Engineering Sciences/Electromagnetism - Keywords : Maxwell's equations – discontinuous Galerkin method – leap-frog time scheme – stability – convergence – non-conforming meshes – high-order accuracy.
- hal-00600467, version 1
- http://hal.archives-ouvertes.fr/hal-00600467
- oai:hal.archives-ouvertes.fr:hal-00600467
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- Submitted on: Wednesday, 15 June 2011 03:34:30
- Updated on: Monday, 26 September 2011 11:35:55
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