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

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

作者机构：School of Mathematics and StatisticsWuhan UniversityWuhan 430072P.R.China Institute of Applied Physics and ComputationalMathematicsBeijing 100094P.R.China Computational Science Hubei Key LaboratoryWuhan UniversityWuhan 430072P.R.China 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2022年第15卷第2期

页      面：484-509页

核心收录：

学科分类：0820[工学-石油与天然气工程] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

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) 

主　　题：Stokes eigenvalue problems divergence-free patch reconstruction discontinuous Galerkin mixed finite element 

摘      要：The discontinuous Galerkin method by divergence-free patch reconstruction is proposed for Stokes eigenvalue *** utilizes the mixed finite element *** patch reconstruction technique constructs two categories of approximation ***,the local divergence-free space is employed to discretize the velocity space,and the pressure space is approximated by standard reconstruction space *** from the divergence-free constraint;the identical element patch serves two approximation spaces while using the element pair Pm+1/*** optimal error estimate is derived under the inf-sup condition *** examples are carried out to validate the inf-sup test and the theoretical results.