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Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 484-509.
Published online: 2022-03
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0085}, url = {http://global-sci.org/intro/article_detail/nmtma/20361.html} }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.