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The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems

The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems

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 L2 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.

Author Details

Di Li Email

Min Liu Email

Xiliang Lu Email

Jerry Zhijian Yang Email