The Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems
Year: 2022
Author: Jerry Zhijian Yang, Di Li, Zhiyuan Sun, Fengru Wang, Jerry Zhijian Yang
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 2 : pp. 484–509
Abstract
The discontinuous Galerkin method by divergence-free patch reconstruction is proposed for Stokes eigenvalue problems. It utilizes the mixed finite element framework. The patch reconstruction technique constructs two categories of approximation spaces. Namely, the local divergence-free space is employed to discretize the velocity space, and the pressure space is approximated by standard reconstruction space simultaneously. Benefit from the divergence-free constraint; the identical element patch serves two approximation spaces while using the element pair $\mathbb{P}^{m+1}/ \mathbb{P}^m$. The optimal error estimate is derived under the inf-sup condition framework. Numerical examples are carried out to validate the inf-sup test and the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2021-0085
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 2 : pp. 484–509
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Stokes eigenvalue problems divergence-free patch reconstruction discontinuous Galerkin mixed finite element.