Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems

DOI10.1515/JNUM.2010.003zbMath1194.65147OpenAlexW2033853442MaRDI QIDQ3564649

Ronald H. W. Hoppe, Huangxin Chen, Xuejun Xu

Publication date: 26 May 2010

Published in: Journal of Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jnum.2010.003

zbMATH Keywords

algorithmsuniform convergencenumerical experimentspreconditioningmultigrid methodadaptive finite element methodsmesh refinementlocal smoothingsecond-order elliptic boundary-value problemsJacobi and Gauss-Seidel smoothinglocal multilevel methodSchwarz theory

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Preconditioners for iterative methods (65F08)

Related Items (11)

Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations ⋮ Local Multilevel Methods with Rectangular Finite Elements for the Biharmonic Problem ⋮ Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation ⋮ An optimal multilevel method with one smoothing step for the Morley element ⋮ An adaptive mesh refinement strategy for finite element solution of the elliptic problem ⋮ An improved multigrid algorithm for \(n\)-irregular meshes with subspace correction smoother ⋮ Stable multilevel splittings of boundary edge element spaces ⋮ Optimal additive Schwarz methods for the \(hp\)-BEM: the hypersingular integral operator in 3D on locally refined meshes ⋮ BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines ⋮ Rate optimality of adaptive finite element methods with respect to overall computational costs ⋮ Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements

Cites Work

• Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems
• Two preconditioners based on the multi-level splitting of finite element spaces
• On the multi-level splitting of finite element spaces
• The hierarchical basis multigrid method
• Multilevel preconditioning
• Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes
• Adaptive finite element methods with convergence rates
• Optimality of a standard adaptive finite element method
• Convergence of the multigrid $V$-cycle algorithm for second-order boundary value problems without full elliptic regularity
• Convergence Estimates for Multigrid Algorithms without Regularity Assumptions
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• A New Convergence Proof for the Multigrid Method Including the V-Cycle
• The Fast Adaptive Composite Grid (FAC) Method for Elliptic Equations
• Local Mesh Refinement Multilevel Techniques
• Local mesh refinement in 2 and 3 dimensions
• Optimal Multilevel Iterative Methods for Adaptive Grids
• Fully Adaptive Multigrid Methods
• Iterative Methods by Space Decomposition and Subspace Correction
• On the Conditioning of Finite Element Equations with Highly Refined Meshes
• The method of alternating projections and the method of subspace corrections in Hilbert space
• Convergence of Adaptive Finite Element Methods
• New Estimates for Multilevel Algorithms Including the V-Cycle

This page was built for publication: Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems