In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L2-norm. In particular, the error in the energy norm is shown to converge with the optimal order O(h^min{s,l}) with respect to the mesh size h, the polynomial degree l, and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L2-error is shown to converge with the optimal order O(h^{l+1}). The theoretical results are confirmed in a series of numerical experiments.
Interior penalty method for the indefinite time-harmonic Maxwell equations
PERUGIA, ILARIA;
2005-01-01
Abstract
In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L2-norm. In particular, the error in the energy norm is shown to converge with the optimal order O(h^min{s,l}) with respect to the mesh size h, the polynomial degree l, and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L2-error is shown to converge with the optimal order O(h^{l+1}). The theoretical results are confirmed in a series of numerical experiments.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.