TY - JOUR
T1 - High-Order Leap-Frog Based Discontinuous Galerkin Method for the Time-Domain Maxwell Equations on Non-Conforming Simplicial Meshes
AU - Hassan Fahs
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 275
EP - 300
PY - 2009
DA - 2009/02
SN - 2
DO - http://doi.org/10.4208/nmtma.2009.m8018
UR - https://global-sci.org/intro/article_detail/nmtma/6026.html
KW - Maxwell's equations, discontinuous Galerkin method, leap-frog time scheme, stability,
convergence, non-conforming meshes, high-order accuracy.
AB - <p style="text-align: justify;">A high-order leap-frog based non-dissipative discontinuous Galerkin time-domain method for solving Maxwell&#39;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 $N$th-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&#39;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.</p>