Residual-based a posteriori error estimator for the mixed finite element approximation of the biharmonic equation

DOI10.1002/num.20524zbMath1223.65087OpenAlexW2149778240WikidataQ115398421 ScholiaQ115398421MaRDI QIDQ3082470

Thirupathi Gudi

Publication date: 10 March 2011

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

Full work available at URL: https://doi.org/10.1002/num.20524

zbMATH Keywords

numerical examplesbiharmonic equationmixed finite elementsa posteriori error control

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Cites Work

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• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• Two-level non-overlapping Schwarz preconditioners for a discontinuous Galerkin approximation of the biharmonic equation
• Mixed discontinuous Galerkin finite element method for the biharmonic equation
• A posteriori error estimates for the Morley plate bending element
• \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
• \(hp\)-version interior penalty DGFEMs for the biharmonic equation
• A posteriori error estimation and adaptive mesh-refinement techniques
• A posteriori error estimates for nonconforming finite element methods
• 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
• Adaptive finite element methods with convergence rates
• Optimality of a standard adaptive finite element method
• Convergence analysis of an adaptive nonconforming finite element method
• A unifying theory of a posteriori finite element error control
• An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• Mixed and Hybrid Finite Element Methods
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
• Data Oscillation and Convergence of Adaptive FEM
• A posteriori error estimators for nonconforming finite element methods
• A Convergent Adaptive Algorithm for Poisson’s Equation
• A posteriori error estimates for finite element approximations of the Cahn-Hilliard equation and the Hele-Shaw flow
• Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems
• The Mathematical Theory of Finite Element Methods
• Error reduction and convergence for an adaptive mixed finite element method
• Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs