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Volume 15, Issue 1
The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems

Di Li, Min Liu, Xiliang Lu & Jerry Zhijian Yang

Adv. Appl. Math. Mech., 15 (2023), pp. 30-48.

Published online: 2022-10

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  • 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.

  • AMS Subject Headings

35J05, 65N30

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COPYRIGHT: © Global Science Press

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@Article{AAMM-15-30, author = {Li , DiLiu , MinLu , Xiliang and Yang , Jerry Zhijian}, title = {The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0008}, url = {http://global-sci.org/intro/article_detail/aamm/21124.html} }
TY - JOUR T1 - The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems AU - Li , Di AU - Liu , Min AU - Lu , Xiliang AU - Yang , Jerry Zhijian JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 30 EP - 48 PY - 2022 DA - 2022/10 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2022-0008 UR - https://global-sci.org/intro/article_detail/aamm/21124.html KW - Least-squares reconstruction, Helmholtz problems, patch reconstruction, discontinuous Galerkin, error estimates. AB -

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.

Li , DiLiu , MinLu , Xiliang and Yang , Jerry Zhijian. (2022). The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems. Advances in Applied Mathematics and Mechanics. 15 (1). 30-48. doi:10.4208/aamm.OA-2022-0008
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