A C 0 finite element method for the biharmonic problem without extrinsic penalization

DOI10.1002/num.21868zbMath1314.65149OpenAlexW1571953545MaRDI QIDQ2875715

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Publication date: 11 August 2014

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.21868

zbMATH Keywords

stabilityconvergencefinite element methodbiharmonic equationnumerical experimentKirchhoff plates

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) 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)

Related Items (12)

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Cites Work

• Unnamed Item
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• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• A weakly over-penalized symmetric interior penalty method for the biharmonic problem
• A new discontinuous Galerkin method for Kirchhoff plates
• \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
• A \(C^0\) discontinuous Galerkin formulation for Kirchhoff plates
• Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
• The Morley element for fourth order elliptic equations in any dimensions
• An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem
• Finite Element Methods for Elliptic Equations Using Nonconforming Elements
• The Mathematical Theory of Finite Element Methods

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