The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems (Advances in Applied Mathematics and Mechanics, 2022)
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-squaresover a neighboring element patch. We prove a prior error estimates in the $L^2$ normand energy norm. For each fixed wave number $k,$ the accuracy and efficiency of themethod up to order five with high-order polynomials. Numerical examples are carriedout to validate the theoretical results.