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

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
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