A two-grid discretization scheme for the Steklov eigenvalue problem

作者：Li Qin^*; Yang Yidu

来源：Journal of Applied Mathematics and Computing, 2011, 36(1-2): 129-139.

DOI：10.1007/s12190-010-0392-9

• Approximate solution
• Asymptotically optimal
• Coarser grid
• Discretization scheme
• Eigenvalue problem
• Error estimates
• Fine grids
• Finite element
• Linear algebraic systems
• Numerical experiments
• Spectral approximations
• Steklov eigenvalue problem
• Two-grid

In the paper, a two-grid discretization scheme is discussed for the Steklov eigenvalue problem. With the scheme, the solution of the Steklov eigenvalue problem on a fine grid is reduced to the solution of the Steklov eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. Using spectral approximation theory, it is shown theoretically that the two-scale scheme is efficient and the approximate solution obtained by the scheme maintains the asymptotically optimal accuracy. Finally, numerical experiments are carried out to confirm the considered theory.

• 出版日期2011
• 单位贵州师范大学