Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator

DOI10.1090/S0025-5718-2011-02551-2zbMath1246.65208MaRDI QIDQ2894508

Joseph E. Pasciak, Andrea Bonito

Publication date: 29 June 2012

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

zbMATH Keywords

convergenceLaplace-Beltrami operatorperturbation analysisnumerical result\(V\)-cycle algorithmsmooth and closed surfacevariational and non-variational multigrid algorithms

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Elliptic equations on manifolds, general theory (58J05)

Related Items (8)

Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator ⋮ A priori error analysis for an isogeometric discontinuous Galerkin approximation for convection problems on surfaces ⋮ On the nodal set of the eigenfunctions of the Laplace-Beltrami operator for bounded surfaces in \(\mathbb R^3\): a computational approach ⋮ A Posteriori Error Estimates for the Laplace--Beltrami Operator on Parametric $C^2$ Surfaces ⋮ High-order AFEM for the Laplace-Beltrami operator: convergence rates ⋮ Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces ⋮ A Priori Error Estimates for Finite Element Approximations to Eigenvalues and Eigenfunctions of the Laplace--Beltrami Operator ⋮ On the controllability of diffusion processes on a sphere: A numerical study

Uses Software

• SG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A finite element method for surface PDEs: Matrix properties
• Finite element methods (Part 1)
• Geometrically Consistent Mesh Modification
• A Finite Element Method for Elliptic Equations on Surfaces
• AFEM for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
• Finite elements on evolving surfaces
• Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
• A Variational Shape Optimization Approach for Image Segmentation with a Mumford–Shah Functional
• A New Convergence Proof for the Multigrid Method Including the V-Cycle
• Uniform Convergence of Multigrid V-Cycle Iterations for Indefinite and Nonsymmetric Problems
• A sharp convergence estimate for the method of subspace corrections for singular systems of equations
• BPX‐type Preconditioners for Second and Fourth Order Elliptic Problems on the Sphere
• An Adaptive Finite Element Method for the Laplace–Beltrami Operator on Implicitly Defined Surfaces
• Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
• The Analysis of Multigrid Algorithms with Nonnested Spaces or Noninherited Quadratic Forms
• Finite element discretization of the Navier-Stokes equations with a free capillary surface
• Mathematical problems in image processing. Partial differential equations and the calculus of variations. Foreword by Olivier Faugeras
• Adaptive numerical treatment of elliptic systems on manifolds

This page was built for publication: Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator