The Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems  

作　　者：Di Li Zhiyuan Sun Fengru Wang Jerry Zhijian Yang 

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China [2]Institute of Applied Physics and ComputationalMathematics,Beijing 100094,P.R.China [3]Computational Science Hubei Key Laboratory,Wuhan University,Wuhan 430072,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2022年第2期484-509,共26页高等学校计算数学学报（英文版）

基　　金：supported by the National Key Research and Development Program of China(Grant No.2020YFA0714200);by the National Natural Science Foundation of China(Grant Nos.12125103,12071362,12101062);the China Postdoctoral Science Foundation(Grant No.2019M660558);by the Natural Science Foundation of Hubei Province(Grant No.2019CFA007)。

摘　　要：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 Pm+1/Pm.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.

关 键 词：Stokes eigenvalue problems DIVERGENCE-FREE patch reconstruction discontinuous Galerkin mixed finite element 

分 类 号：O17[理学—数学]