A conjugate gradient method and a multigrid algorithm for Morley's finite element approximation of the biharmonic equation

DOI10.1007/BF01408577zbMath0595.65113OpenAlexW2063483315MaRDI QIDQ1077900

Dietrich Braess, Petra Peisker

Publication date: 1987

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133173

zbMATH Keywords

convergencenumerical resultspreconditioningbiharmonic equationstepsize controlPoisson equationsmultigrid algorithmpreconditioned conjugate gradient methodsnonconforming finite elementsMorley's nonconforming displacement method

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Iterative numerical methods for linear systems (65F10) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Cites Work

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• On nonconforming an mixed finite element methods for plate bending problems. The linear case
• On the boundary value problem of the biharmonic operator on domains with angular corners
• An Optimal Order Process for Solving Finite Element Equations
• Analysis of Mixed Methods Using Mesh Dependent Norms
• On the Numerical Solution of the Biharmonic Equation and the Role of Squaring Matrices for Preconditioning