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.
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)。