In this paper, we consider some multigrid algorithms for the biharmonic problem discretized by Morley element on nonnested meshes. Through taking the averages of the nodal variables we construct an intergrid transfer ...In this paper, we consider some multigrid algorithms for the biharmonic problem discretized by Morley element on nonnested meshes. Through taking the averages of the nodal variables we construct an intergrid transfer operator that satisfies a certain stable approximation property. The so-called regularity-approximation assumption is then established. Optimal convergence properties of the W-cycle and a uniform condition number estimate for the variable V-cycle preconditioner are presented. This technique is applicable to other nonconforming plate elements.展开更多
文摘In this paper, we consider some multigrid algorithms for the biharmonic problem discretized by Morley element on nonnested meshes. Through taking the averages of the nodal variables we construct an intergrid transfer operator that satisfies a certain stable approximation property. The so-called regularity-approximation assumption is then established. Optimal convergence properties of the W-cycle and a uniform condition number estimate for the variable V-cycle preconditioner are presented. This technique is applicable to other nonconforming plate elements.
