Convergence of \(V\)-cycle and \(F\)-cycle multigrid methods for the biharmonic problem using the Morley element. (English) Zbl 1065.65139

Zhao, Jie

ETNA, Electron. Trans. Numer. Anal. 17, 112-132 (2004).

Summary: Multigrid \(V\)-cycle and \(F\)-cycle algorithms for the bibarmonic problem using the Morley element are studied in this paper. We show that the contraction numbers can be uniformly improved by increasing the number of smoothing steps.

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
31A30	Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
35J40	Boundary value problems for higher-order elliptic equations

Keywords:

multigrid; nonconforming; \(V\)-cycle; \(F\)-cycle; biharmonic problem; Morley element