Year: 2023
Author: Di Li, Min Liu, Xiliang Lu, Jerry Zhijian Yang
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 1 : pp. 30–48
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0008
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 1 : pp. 30–48
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Least-squares reconstruction Helmholtz problems patch reconstruction discontinuous Galerkin error estimates.