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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
Citations
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Dissertation
Méthodologie d analyse de fiabilité basée sur des techniquesheuristiques d optimisation et modèles sans maillage : applications aux systèmes mécaniques
TL;DR: In this paper, a methode d'analyse de fiabilite basee sur des techniques d'optimisation heuristiques (HBRM, Heuristic-based Reliability Method) configure the methodologie de conception fiabiliste proposee dans ce memoire.
Dissertation
Numerical modelling of complex geomechanical problems
TL;DR: In this article, the authors focus on the treatment of large boundary displacements by means of Arbitrary Lagrangian-Eulerian (ALE) formulations, and the numerical solution of highly nonlinear systems of equations in solid mechanics.
Error estimation and adaptive spatial discretisation for quasi-brittle failure
TL;DR: In this article, two failure models have been investigated based on a residual-type error estimate, in the form of either energy norm or the quantity of interest, discretization factors and various adaptive discretisation schemes have been examined.
Book ChapterDOI
A coupled FE-model for tunneling by means of compressed air
TL;DR: In this paper, the development and the application of a coupled numerical model for tunnelling below the groundwater table, taking into account compressed air as a means for displacing the groundwater in the vicinity of the tunnel face, is discussed.
References
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Journal ArticleDOI
A simple error estimator and adaptive procedure for practical engineerng analysis
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.
Journal ArticleDOI
A‐posteriori error estimates for the finite element method
Ivo Babuška,Werner C. Rheinboldt +1 more
TL;DR: In this article, a-posteriori error estimates for finite element solutions are derived in an asymptotic form for h 0 where h measures the size of the elements.
Journal ArticleDOI
Adaptive remeshing for compressible flow computations
TL;DR: An adaptive mesh procedure for improving the quality of steady state solutions of the Euler equations in two dimensions is described, implemented in conjunction with a finite element solution algorithm, using linear triangular elements, and an explicit time-stepping scheme.
Journal ArticleDOI
Some a posteriori error estimators for elliptic partial differential equations
Randolph E. Bank,A. Weiser +1 more
TL;DR: Three new a posteriori error estimators in the energy norm for finite element solutions to elliptic partial differential equations are presented and it is proved that as the mesh size decreases, under suitable assumptions, two of the error estimator approach upper bounds on the norm of the true error.
Journal ArticleDOI
A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. part II: computational aspects
TL;DR: In this article, the authors proposed a hyperelastic J2-flow theory for elastoplastic tangent moduli, which reduces to a trivial modification of the classical radial return algorithm which is amenable to exact linearization.
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