An Iterative Finite Element Method for Approximating the Biharmonic Equation

DOI10.2307/2008758zbMath0699.73052OpenAlexW4240982329MaRDI QIDQ3478068

Peter B. Monk

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2008758

zbMATH Keywords

conjugate gradient methodmixed finite element methodclamped platesimply supportedsequence of Dirichlet problems for Poisson's equation

Mathematics Subject Classification ID

Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Cites Work

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• Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations
• Dual iterative techniques for solving a finite element approximation of the biharmonic equation
• On the convergence of a mixed finite-element method for plate bending problems
• Two mixed finite element methods for the simply supported plate problem
• A Mixed Finite Element Method for the Biharmonic Equation
• Numerical Methods for the First Biharmonic Equation and for the Two-Dimensional Stokes Problem
• The Lagrange Multiplier Method for Dirichlet's Problem
• Higher Order Approximations to the Boundary Conditions for the Finite Element Method
• Interpolated Boundary Conditions in the Finite Element Method
• Approximation of the Biharmonic Equation by a Mixed Finite Element Method
• Simultaneous Approximation in Scales of Banach Spaces
• On $L^p$ Estimates and Regularity II.

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