TY - JOUR
T1 - The Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems
AU - Li , Di
AU - Sun , Zhiyuan
AU - Wang , Fengru
AU - Yang , Jerry Zhijian
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 484
EP - 509
PY - 2022
DA - 2022/03
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2021-0085
UR - https://global-sci.org/intro/article_detail/nmtma/20361.html
KW - Stokes eigenvalue problems, divergence-free, patch reconstruction, discontinuous Galerkin, mixed finite element.
AB - <p style="text-align: justify;">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.</p>