Acceleration Of Two-Level Stabilized Mixed Finite Element Method To Solve The Stokes Eigenvalue Problem

In the paper, we propose the accelerated two-level stabilized mixed finite element method for the Stokes eigenvalue problem. In order to improve the accuracy degree, we solve the Stokes eigenvalue problem by P2- P2 element. And we use the pressure projection method to make the bilinear form satisfying the discrete inf-sup condition. For solving eigenvalue problems is a very complicated process, two-level method is used to improve the computing speed. The main steps are to solve a Stokes eigenvalue problem in a coarse grid, then solve a Stokes problem in a fine mesh, finally apply the shift-inverse method to obtain the approximate eigenvalue. Also, we give the optimal order estimates and some numerical examples to verify the theoretical results.