Volume 12, Issue 3
A Discontinuous Galerkin Method by Patch Reconstruction for Convection-Diffusion Problems

Zhiyuan Sun, Jun Liu & Pei Wang

Adv. Appl. Math. Mech., 12 (2020), pp. 729-747.

Published online: 2020-04

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  • Abstract

In this article, we apply the discontinuous Galerkin method by patch reconstruction for solving convection-diffusion problems. The proposed method is highly efficient that it uses only one degree of freedom per element to achieve higher order approximation. It also enjoys the implementation flexibility on the general polygonal meshes. A priori error estimates of energy norm is devised. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method.

  • Keywords

Convection-diffusion problem, polygonal mesh, discontinuous Galerkin method, patch reconstruction.

  • AMS Subject Headings

49N45, 65N21

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zysun.math@gmail.com (Zhiyuan Sun)

caepcfd@126.com (Jun Liu)

wangpei@iapcm.ac.cn (Pei Wang)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-12-729, author = {Sun , Zhiyuan and Liu , Jun and Wang , Pei}, title = {A Discontinuous Galerkin Method by Patch Reconstruction for Convection-Diffusion Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {3}, pages = {729--747}, abstract = {

In this article, we apply the discontinuous Galerkin method by patch reconstruction for solving convection-diffusion problems. The proposed method is highly efficient that it uses only one degree of freedom per element to achieve higher order approximation. It also enjoys the implementation flexibility on the general polygonal meshes. A priori error estimates of energy norm is devised. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0193}, url = {http://global-sci.org/intro/article_detail/aamm/16421.html} }
TY - JOUR T1 - A Discontinuous Galerkin Method by Patch Reconstruction for Convection-Diffusion Problems AU - Sun , Zhiyuan AU - Liu , Jun AU - Wang , Pei JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 729 EP - 747 PY - 2020 DA - 2020/04 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0193 UR - https://global-sci.org/intro/article_detail/aamm/16421.html KW - Convection-diffusion problem, polygonal mesh, discontinuous Galerkin method, patch reconstruction. AB -

In this article, we apply the discontinuous Galerkin method by patch reconstruction for solving convection-diffusion problems. The proposed method is highly efficient that it uses only one degree of freedom per element to achieve higher order approximation. It also enjoys the implementation flexibility on the general polygonal meshes. A priori error estimates of energy norm is devised. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method.

Zhiyuan Sun, Jun Liu & Pei Wang. (2020). A Discontinuous Galerkin Method by Patch Reconstruction for Convection-Diffusion Problems. Advances in Applied Mathematics and Mechanics. 12 (3). 729-747. doi:10.4208/aamm.OA-2019-0193
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