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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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A gradient‐based adaptation procedure and its implementation in the element‐free Galerkin method
TL;DR: A gradient-based adaptation procedure that is implemented in the element-free Galerkin method for linear elasto-static problems, guided by the gradient of strain energy density, based on the assumption: a larger gradient needs a richer mesh and vice versa.
Journal ArticleDOI
Novel quadtree algorithm for adaptive analysis based on cell-based smoothed finite element method
TL;DR: A novel adaptive technique is developed that combines a newly developed quadtree algorithm with the cell-based smoothed finite element method (CS-FEM) for automatic mesh adaptation using quadrilateral elements for more proficient analysis of complex geometry.
Journal ArticleDOI
Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems
TL;DR: This paper presents an adaptive refinement strategy based on a hierarchical element subdivision dedicated to modelling elastoplastic materials in transient dynamics that optimizes the computational cost of the solution on the finest localized mesh.
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Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations
TL;DR: Three-dimensional results using the adaptive multigrid strategy on elastoplastic structures in transient dynamics and in a linear geometrical framework are presented.
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Alternative mesh optimality criteria for h-adaptive finite element method
TL;DR: The use of alternative mesh optimality criteria with an h-adaptive procedure for 2D elastic problems is proposed and an efficient adaptive technique which automatically takes account the steep gradient areas is proposed.
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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