Year: 2023
Author: Ling Ling Sun, Hai Bi, Yidu Yang
Communications in Computational Physics, Vol. 34 (2023), Iss. 5 : pp. 1391–1419
Abstract
In this paper, based on the velocity-pressure formulation of the Stokes eigenvalue problem in $d$-dimensional case $(d=2,3),$ we propose a multigrid discretization of discontinuous Galerkin method using $\mathbb{P}_k−\mathbb{P}_{k−1}$ element $(k≥1)$ and prove its a priori error estimate. We also give the a posteriori error estimators for approximate eigenpairs, prove their reliability and efficiency for eigenfunctions, and also analyze their reliability for eigenvalues. We implement adaptive calculation, and the numerical results confirm our theoretical predictions and show that our method is efficient and can achieve the optimal convergence order $\mathcal{O}(do f^{ \frac{−2k}{d}} ).$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0027
Communications in Computational Physics, Vol. 34 (2023), Iss. 5 : pp. 1391–1419
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Stokes eigenvalue problem discontinuous Galerkin method multigrid discretizations adaptive algorithm.