Adv. Appl. Math. Mech., 15 (2023), pp. 30-48.
Published online: 2022-10
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0008}, url = {http://global-sci.org/intro/article_detail/aamm/21124.html} }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.