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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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Journal ArticleDOI
Quantification of blood flow velocity in stenosed arteries by the use of finite elements: an observer-independent noninvasive method
Hannes Mühlthaler,Bernhard Quatember,Gustav Fraedrich,Markus Mühlthaler,Bernhard Pfeifer,Andreas Greiner,Michael Schocke +6 more
TL;DR: A methodology to noninvasively perform numerical simulations of a patient's hemodynamic state on the basis of magnetic resonance images and by the means of the finite element method is developed.
Journal ArticleDOI
Recovery strategies, a posteriori error estimation, and local error indication for second‐order G/XFEM and FEM
TL;DR: In this article , the authors proposed a block-diagonal Zienkiewicz-Zhu (ZZ•BD) a posteriori error estimator for second-order G/XFEM and FEM approximations.
Journal ArticleDOI
Knowledge base for controlled cost and quality of finite element modelling
TL;DR: The paper presents the use and the building of a consultative knowledge base (KB) for FEA that was built mainly by the use of the Design of Experiments method and aims to reuse past design and analysis work as analysis template.
Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería
TL;DR: In this article, a finite element moving mesh algorithm has been developed in order to integrally move a part of the mesh following a moving load, which has been validated with the analytical solution of the moving load applied on a simply supported beam.
Journal ArticleDOI
Unified hp-HDG Frameworks for Friedrichs' PDE systems
TL;DR: In this article , a unified $hp$-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations of Friedrichs' type 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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