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Adaptive finite element strategies based on error assessment
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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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Journal ArticleDOI
Anisotropic mesh adaptation for region-based segmentation accounting for image spatial information
TL;DR: In this article , a finite element-based image segmentation strategy enhanced by an anisotropic mesh adaptation procedure is presented, which relies on a split-adapt Bregman algorithm for the minimisation of a region-based energy functional and on a recovery-based error estimate to drive mesh adaptation.
Dissertation
Modélisation mathématique et simulation numérique de l'hydrodynamique : cas des inondations en aval du barrage de Diama
TL;DR: Le delta du fleuve Senegal est le theâtre de crues importantes, le plus souvent catastrophiques et la derniere en date a necessite l'ouverture d'une breche dans la Langue de Barbarie which est une fine bande de sable separant le delta duFleuve de la mer.
DatasetDOI
Open data for paper "Efficient implementation of high-order finite elements for Helmholtz problems"
TL;DR: This repository contains the open data associated with the journal paper titled "Efficient implementation of high-order finite elements for Helmholtz problems" by Hadrien Be?riot, Albert Prinn and Gwe?nae?l Gabard published in the International Journal for Numerical Methods in Engineering.
Large deformation analysis in geomechanics using adaptive finite element methods
TL;DR: This chapter discusses Adaptive finite element methods and their applications in the context of finite element adequacy, as well as some of the approaches taken in this chapter.
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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