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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
Citations
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Journal ArticleDOI
Efficient unstructured quadrilateral mesh generation
Josep Sarrate,Antonio Huerta +1 more
TL;DR: This work is devoted to the description of an algorithm for automatic quadrilateral mesh generation which automatically generates meshes composed entirely by quadrilaterals over complex geometries and induces an efficient data structure which optimizes the computer cost.
Journal ArticleDOI
Efficient implementation of high-order finite elements for Helmholtz problems
TL;DR: An efficient implementation of the high‐order finite element method (FEM) for tackling large‐scale engineering problems arising in acoustics with the ability to select automatically the order of interpolation in each element so as to obtain a target accuracy while minimizing the cost.
Journal ArticleDOI
Arbitrary Lagrangian-Eulerian (ALE) formulation for hyperelastoplasticity
TL;DR: In this paper, an extension to hyperelastic-plastic models is presented, where the deformed configuration at the beginning of the time-step, not the initial undef ormed configuration, is chosen as the reference configuration.
Journal ArticleDOI
An ALE formulation based on spatial and material settings of continuum mechanics. Part 2: Classification and applications
TL;DR: In this article, a specialisation of the generic hyperelastic arbitrary Lagrangian-Eulerian (ALE) formulation derived in Part 1 is made of the NeuHookean material, which is shown that with the proposed ALE formulation, potential energies can be obtained that are minimum for the considered topology.
Journal ArticleDOI
Error estimation and adaptivity for nonlocal damage models
TL;DR: In this paper, an adaptive strategy based on error estimation is proposed to ensure the quality of the FE solution, which is based on the combination of a residual-type error estimator and quadrilateral h -remeshing.
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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