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Adaptive finite element strategies based on error assessment
TLDR
Two main ingredients are needed for adaptive finite element computations: the error of a given solution must be assessed, and a new spatial discretization must be defined via h-, p- or r-adaptivity.Abstract:
Two main ingredients are needed for adaptive finite element computations. First, the error of a given solution must be assessed, by means of either error estimators or error indicators. After that, a new spatial discretization must be defined via h-, p- or r-adaptivity. In principle, any of the approaches for error assessment may be combined with any of the procedures for adapting the discretization. However, some combinations are clearly preferable. The advantages and limitations of the various alternatives are discussed. The most adequate strategies are illustrated by means of several applications in solid mechanics. Copyright © 1999 John Wiley & Sons, Ltd.read more
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Reference EntryDOI
Arbitrary Lagrangian–Eulerian Methods
TL;DR: In this paper, the authors provide an in-depth survey of arbitrary Lagrangian-Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details.
Journal ArticleDOI
Characterisation of materials subjected to large strains by inverse modelling based on in-plane displacement fields
Jörgen Kajberg,Göran Lindkvist +1 more
TL;DR: In this article, a method for characterisation of materials subjected to large strains beyond the levels when plastic instability occurs in standard tension tests is presented, where thin sheets of two types of hot-rolle...
Journal ArticleDOI
Numerical modelling of welding
TL;DR: In this article, the application of the finite element method to predict the thermal, material and mechanical effects of welding is described, and some recent applications are reviewed and future developments are discussed.
Journal ArticleDOI
Review: A posteriori error estimation techniques in practical finite element analysis
TL;DR: The basic concepts to obtain a posteriori error estimates for the finite element solution of an elliptic linear model problem are reviewed and it is concluded that the actually practical error estimation techniques do not provide mathematically proven bounds on the error and need to be used with care.
Journal ArticleDOI
Enrichment and coupling of the finite element and meshless methods
TL;DR: In this paper, a mixed hierarchical approximation based on finite elements and meshless methods is presented, which couples regions where finite elements or meshless method are used to interpolate: continuity and consistency is preserved.
References
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Book
Moving finite elements
TL;DR: This book brings together most of the work done over the last decade or so which has been stimulated by Miller's original idea, and discusses the interrelationships between the techniques and the established ideas of the method of characteristics, Hamilton's equations, the Legendre transformation, and grid equidistribution.
Journal ArticleDOI
Error estimation and mesh optimization for classical finite elements
TL;DR: Several applications for 2D or axisymmetric elasticity problems of a method to control the quality of a finite element computation, and to optimize the choice of meshes are presented.
Journal ArticleDOI
A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method
TL;DR: In this paper, the authors studied the pollution-error in the h-version of the finite element method and its effect on the quality of the local error indicators in the interior of the mesh.
Journal ArticleDOI
A procedure for a posteriori error estimation for h-p finite element methods
Mark Ainsworth,J. Tinsley Oden +1 more
TL;DR: Results show that the approach is applicable to general linearly elliptic systems, including unsymmetrical operators, and that the method is valid for broad classes of linear and non-linear problems.
Journal ArticleDOI
H-adaptive finite element methods for dynamic problems, with emphasis on localization
Ted Belytschko,Mazen R. Tabbara +1 more
TL;DR: In this article, various error criteria are examined and it is shown that for problems involving plastic response or localization, an error criterion based on an L 2 -projection of strains is the most effective for the constant strain elements considered here.
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