The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems

Abstract

. This paper develops and analyzes interior penalty discontinuous Galerkin (IPDG) method by patch reconstruction technique for Helmholtz problems. The technique achieves high order approximation by locally solving a discrete least-squares over a neighboring element patch. We prove a prior error estimates in the L 2 norm and energy norm. For each fixed wave number k , the accuracy and efficiency of the method up to order five with high-order polynomials. Numerical examples are carried out to validate the theoretical results.