@Article{NMTMA-15-2,
author = {Zhijian, Yang, Jerry and Li, Di and Zhiyuan, Sun and Wang, Fengru and Zhijian, Yang, Jerry},
title = {The Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2022},
volume = {15},
number = {2},
pages = {484--509},
abstract = {<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>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2021-0085},
url = {https://global-sci.com/article/90260/the-discontinuous-galerkin-method-by-divergence-free-patch-reconstruction-for-stokes-eigenvalue-problems}
}