An Adaptive Inverse Iteration And Subspace Iteration Finite Element Algorithm For Stokes Eigenvalue Problems

In this paper,an adaptive inverse iterative?inverse power method?Mixed fi-nite element method and a multi-level subspace iterative method are designed for theStokeseigenvalue problem.The P₂-P₀ mixed finite element space is used.First,theStokesequation boundary value problem is given.The discrete variation-al problem of mixed finite element method is solved by solving the linear algebraic equations on the grid using the multigrid method with LSC-DGS smoother.The experimental results show that this method can achieve optimal linear workload,ie The number of iterations has nothing to do with the problem size.Then an adap-tive inverse iterative algorithm based on the residual posterior error indicator is designed for theStokeseigenvalue problem.Numerical experiments show that the adaptive inverse iterative algorithm is better than the multi-level inverse The iter-ative algorithm for the solution singularity problem.which can improve the overall precision of the numerical solution and can solve the local singularity in the problem calculation.Finally,the multi-level subspace iteration method for solving multiple eigenvalues ofStokeseigenvalue problem is given,and the grid is automatically en-crypted by the given error limit.A multi-grid fast algorithm based on LSC-DGS smoother is added to the multi-level subspace iteration method.The numerical ex-periments show that the eigenvalues obtained by uniform refined grids are closer to the true eigenvalues.Also show this algorithm is fast and effective,which can achieve optimal linear workload.