TY - JOUR
T1 - A Multigrid Discretization of Discontinuous Galerkin Method for the Stokes Eigenvalue Problem
AU - Sun , Ling Ling
AU - Bi , Hai
AU - Yang , Yidu
JO - Communications in Computational Physics
VL - 5
SP - 1391
EP - 1419
PY - 2023
DA - 2023/12
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0027
UR - https://global-sci.org/intro/article_detail/cicp/22257.html
KW - Stokes eigenvalue problem, discontinuous Galerkin method, multigrid discretizations, adaptive algorithm.
AB - <p style="text-align: justify;">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 $\mathcal{O}(do f^{ \frac{−2k}{d}} ).$</p>