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Journal ArticleDOI

Adaptive finite element strategies based on error assessment

TL;DR: 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.

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Citations
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Journal ArticleDOI
01 Jan 2001
TL;DR: In this paper, an adaptive finite element strategy for nonlocal damage computations is presented based on the combination of a residual-type error estimator and quadrilateral h-remeshing.
Abstract: ABSTRACT An adaptive finite element strategy for nonlocal damage computations is presented. The proposed approach is based on the combination of a residual-type error estimator and quadrilateral h-remeshing. A distinctive feature of the error estimator is that it consists in solving simple local problems over elements and so-called patches. The paper focuses on how the nonlocality of the constitutive model should be accounted for when solving these local problems. It is shown that the nonlocal damage models must be slightly modified. The resulting adaptive strategy is illustrated by means of some numerical examples involving the single-edge notched beam test.

12 citations

Journal Article
TL;DR: In this paper, an adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented, which is illustrated by a complex nonlinear problem: the failure analysis of a single-edge notched beam.
Abstract: An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear problem: the failure analysis of a single-edge notched beam. The quasi-brittle response of concrete is modelled by means of a nonlocal damage model.

11 citations


Cites background from "Adaptive finite element strategies ..."

  • ...The error estimator is based on simple local computations over the elements and the so-called patches....

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  • ...Keywords: finite elements, error estimation, adaptivity, nonlinearity, quality of FE solutions, damage models...

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Journal ArticleDOI
TL;DR: This paper overviews a systematic approach for minimizing the time required for finite element analysis (FEA) while achieving a desired level of accuracy in the simulations.

11 citations

Journal ArticleDOI
TL;DR: An object-oriented framework for numerical analysis of multi-physics applications is presented and it was tested for several classical cases involving heat transfer, fluid mechanics and structural mechanics.

10 citations

Dissertation
17 Dec 2012
TL;DR: Au cours de cette these, nous nous sommes interesses a la modelisation des interactions fluide-structure entre un fluide visqueux, incompressible et une structure pouvant etre deformable, pour determiner la loi de nage optimale pour une geometrie de poisson donnee.
Abstract: Au cours de cette these, nous nous sommes interesses a la modelisation des interactions fluide-structure entre un fluide visqueux, incompressible et une structure pouvant etre deformable. Apres avoir presente les differentes approches possibles de modelisation, nous introduisons une nouvelle methode de type frontiere immergee : la methode IPC ("Image Point Correction"). Combinant approches Ghost-Cell et Penalisation, cette methode mixte du second degre globalement et localement en vitesse, est validee sur differents cas tests (comparaisons des coefficients aerodynamiques pour des cylindres fixes ou mobiles, sedimentation 2D d'un cylindre). Nous avons ensuite applique la methode IPC a la simulation de la nage. Dans un premier temps, le solveur 2D a ete couple avec un algorithme d'optimisation mathematique afin de determiner la loi de nage optimale pour une geometrie de poisson donnee. Puis, dans un second temps, nous avons simule la nage 3D apres reconstruction approchee de la geometrie, basee sur des images du nageur. Enfin, grâce a l'outil du squelette, une reconstruction realiste du poisson est proposee.

8 citations


Additional excerpts

  • ...Des études sur l’utilisation de la méthode ALE comme technique d’adaptation de maillage ont été effectuées dans le domaine de la mécanique des solides [55] [5] [6] [88]....

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References
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Journal ArticleDOI
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.
Abstract: 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. The estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials. When combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable. Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.

2,449 citations

Journal ArticleDOI
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.
Abstract: Computable 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. The approach has similarity to the residual method but differs from it in the use of norms of negative Sobolev spaces corresponding to the given bilinear (energy) form. For clarity the presentation is restricted to one-dimensional model problems. More specifically, the source, eigenvalue, and parabolic problems are considered involving a linear, self-adjoint operator of the second order. Generalizations to more general one-dimensional problems are straightforward, and the results also extend to higher space dimensions; but this involves some additional considerations. The estimates can be used for a practical a-posteriori assessment of the accuracy of a computed finite element solution, and they provide a basis for the design of adaptive finite element solvers.

1,211 citations

Journal ArticleDOI
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.

1,079 citations

Journal ArticleDOI
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.
Abstract: We present three new a posteriori error estimators in the energy norm for finite element solutions to elliptic partial differential equations. The estimators are based on solving local Neumann problems in each element. The estimators differ in how they enforce consistency of the Neumann problems. We prove that as the mesh size decreases, under suitable assumptions, two of the error estimators approach upper bounds on the norm of the true error, and all three error estimators are within multiplicative constants of the norm of the true error. We present numerical results in which one of the error estimators appears to converge to the norm of the true error.

815 citations

Journal ArticleDOI
Juan C. Simo1
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.

475 citations