Superconvergence two-grid scheme based on shifted-inverse power method for eigenvalue problems by function value recovery

In the paper, an improved two-grid scheme based on shifted-inverse power method is proposed to solve the elliptic eigenvalue problems. With this new scheme, the solution of the elliptic eigenvalue problem on a fine grid Th is reduced to the solution of the elliptic eigenvalue problem and the recovered eigenfunction on a much coarser grid TH, and the solution of an elliptic boundary value problem and the recovered solution on the fine grid Th. Theoretical analysis shows that the scheme allows a much coarser mesh to achieve the superconvergence rate. Finally, some numerical experiments are carried out to confirm the theoretical analysis.