An improved two-grid finite element method for the Steklov eigenvalue problem

A combination method of finite element method and accelerated two-grid scheme is constructed for solving numerically the two-dimensional Steklov eigenvalue problem. This algorithm involves solving a small Steklov eigenvalue problem on the coarse mesh with mesh size H and a linear algebraic system on the fine mesh with mesh size h. By solving a slightly different linear problem on the fine grid, the computation will be more effective and convenient and the scaling between H and h   becomes h=O(H4)h=O(H4), which can save a large amount of computational time. Finally, numerical tests confirm the theoretical results of the presented method.