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

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.