Theoretical formulations for adaptive finite element computations

DOI10.1002/cnm.1640111010zbMath0848.65078OpenAlexW1990352758MaRDI QIDQ4854729

I. Applegarth, John W. Bull, P. Bettess, T. J. Bond, Long-Yuan Li

Publication date: 11 December 1995

Published in: Communications in Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cnm.1640111010

zbMATH Keywords

numerical examplesadaptive finite element methodmesh refinementerror estimate meshReissner-Mindlin plate bending

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

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Cites Work

• The superconvergent patch recovery (SPR) and adaptive finite element refinement
• The three R's of engineering analysis and error estimation and adaptivity
• Superconvergent patch recovery techniques - some further tests
• Error estimates and adaptive refinement for plate bending problems
• A simple error estimator and adaptive procedure for practical engineerng analysis
• Adaptive techniques in the finite element method
• A robust triangular plate bending element of the Reissner-Mindlin type
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• A three-dimensional adaptive finite element strategy
• Patch recovery based on superconvergent derivatives and equilibrium
• A general methodology for structural shape optimization problems using automatic adaptive remeshing
• Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements
• Error estimates for finite element solutions of elliptic boundary value problems
• Validation of a posteriori error estimators by numerical approach
• Local and global smoothing of discontinuous finite element functions using a least squares method
• On the calculation of consistent stress distributions in finite element approximations
• Note on an approximate method for computing consistent conjugate stresses in elastic finite elements

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