SIAM Journal on Numerical Analysis · 2002 · 18 citations · 20 references
EngineeringComputational EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsConvergence AnalysisFinite Element DiscretizationFinite Element FormulationMesh AnalysisPlate AnalysisPlate ElementsConvergence Rate AnalysisElement FormulationFinite Element Methods For PlatesMesh SizeMultigrid ConvergenceNonconforming Plate ElementsPlate Finite Element AnalysisPreconditioning Techniques
In this paper, a multigrid algorithm is presented for the mortar element method for the Morley nonconforming plate element. Based on the multigrid theory developed by Bramble, Pasciak, and Xu in [Math. Comp., 56 (1991), pp. 1--34], we prove that the W-cycle multigrid method is optimal, i.e., the convergence rate is independent of the mesh size and mesh level. Moreover, a variable V-cycle multigrid preconditioner is constructed, which results in a preconditioned system with a uniformly bounded condition number.
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