A Multigrid Discretization of Discontinuous Galerkin Method for the Stokes Eigenvalue Problem  

作　　者：Ling Ling Sun Hai Bi Yidu Yang 

机构地区：[1]School of Mathematical Sciences,Guizhou Normal University,Guiyang,550001,China [2]School of Biology and Engineering,Guizhou Medical University,Guiyang,550001,China

出　　处：《Communications in Computational Physics》2023年第10期1391-1419,共29页计算物理通讯（英文）

基　　金：supported by the National Natural Science Foundation of China(Nos.12261024,11561014);the Science and Technology Planning Project of Guizhou Province(Guizhou Kehe fundamental research-ZK[2022]No.324).

摘　　要：In this paper,based on the velocity-pressure formulation of the Stokes eigenvalue problemin d-dimensional case(d=2,3),we propose amultigrid discretization of discontinuous Galerkin method using P_(k)-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 O(do f-2k/d).

关 键 词：Stokes eigenvalue problem discontinuous Galerkin method multigrid discretizations adaptive algorithm 

分 类 号：O24[理学—计算数学]