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Multigrid methods for the symmetric interior penalty method on graded meshes
44
Citations
32
References
2009
Year
Numerical AnalysisMathematical ProgrammingSymmetric Interior PenaltyEngineeringMechanical EngineeringComputer-aided DesignStructural OptimizationComputational MechanicsMesh OptimizationNumerical ComputationGraded MeshesComputational GeometryBoundary Element MethodMethod Of Fundamental SolutionUnstructured Mesh GenerationSip MethodFinite Element MethodMultigrid MethodsGrid Optimization
Abstract The symmetric interior penalty (SIP) method on graded meshes and its fast solution by multigrid methods are studied in this paper. We obtain quasi‐optimal error estimates in both the energy norm and the L 2 norm for the SIP method, and prove uniform convergence of the W ‐cycle multigrid algorithm for the resulting discrete problem. The performance of these methods is illustrated by numerical results. Copyright © 2009 John Wiley & Sons, Ltd.
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