Local discontinuous Galerkin methods for the carpet cloak model

Abstract

. The DG methods have been shown to have good performance in numerical simulations of the carpet cloak model in [32]. However, the stability analysis and the error estimate are left to be done. In this paper, we introduce the leap-frog DG methods to solve the carpet cloak model. We prove the stability of the semi-discrete scheme, the sub-optimal error estimate for unstructured meshes, and the optimal error estimate for tensor-product meshes. Then, the fully discrete scheme is stated and the stability is proved. Finally, the numerical accuracy tests on rectangular and triangular meshes are given respectively, and the results of numerical simulations of the wave propagation in the carpet cloak model using the DG scheme are presented.