Multigrid methods for the biharmonic problem discretized by conformingC1finite elements on nonnested meshes∗

DOI10.1080/01630569508816649zbMath0842.65081OpenAlexW2157794520WikidataQ126243157 ScholiaQ126243157MaRDI QIDQ4863081

Xuejun Zhang, James H. Bramble

Publication date: 5 August 1996

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569508816649

zbMATH Keywords

convergencefinite elementsmultigrid algorithmsbiharmonic problemW-cycleuniform condition number estimateV-cycle preconditioner

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for higher-order elliptic equations (35J40) 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) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (12)

New implementation of elliptic systems method for time dependent diffusion tomography with back reflected and transmitted boundary data ⋮ Isoparametric multigrid method for reaction-diffusion equations on two-dimensional domains ⋮ Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems ⋮ Multigrid methods for Hellan-Herrmann-Johnson mixed method of Kirchhoff plate bending problems ⋮ Optimal multilevel adaptive FEM for the Argyris element ⋮ Superconvergent postprocessing of the \(C^1\)-conforming finite element method for fourth-order boundary value problems ⋮ Local Multilevel Methods with Rectangular Finite Elements for the Biharmonic Problem ⋮ An optimal multilevel method with one smoothing step for the Morley element ⋮ Preconditioning high order \(H^2\) conforming finite elements on triangles ⋮ A C1-P2 finite element without nodal basis ⋮ A cubic Hermite finite element-continuation method for numerical solutions of the von Kármán equations ⋮ A \(V\)-cycle multigrid method and additive multilevel preconditioners for the plate bending problem discretized by conforming finite elements

Cites Work

• Unnamed Item
• A multilevel algorithm for the biharmonic problem
• A conjugate gradient method and a multigrid algorithm for Morley's finite element approximation of the biharmonic equation
• An optimal order multigrid method for biharmonic, \(C^ 1\) finite element equations
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Multigrid Preconditioning for the Biharmonic Dirichlet Problem
• Piecewise Quadratic Approximations on Triangles
• Multilevel Schwarz Methods for the Biharmonic Dirichlet Problem
• An Optimal-Order Nonconforming Multigrid Method for the Biharmonic Equation

This page was built for publication: Multigrid methods for the biharmonic problem discretized by conformingC¹finite elements on nonnested meshes^∗