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.