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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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Arbitrary Lagrangian–Eulerian Methods
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Characterisation of materials subjected to large strains by inverse modelling based on in-plane displacement fields
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TL;DR: In this article, a method for characterisation of materials subjected to large strains beyond the levels when plastic instability occurs in standard tension tests is presented, where thin sheets of two types of hot-rolle...
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Numerical modelling of welding
TL;DR: In this article, the application of the finite element method to predict the thermal, material and mechanical effects of welding is described, and some recent applications are reviewed and future developments are discussed.
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Review: A posteriori error estimation techniques in practical finite element analysis
TL;DR: The basic concepts to obtain a posteriori error estimates for the finite element solution of an elliptic linear model problem are reviewed and it is concluded that the actually practical error estimation techniques do not provide mathematically proven bounds on the error and need to be used with care.
Journal ArticleDOI
Enrichment and coupling of the finite element and meshless methods
TL;DR: In this paper, a mixed hierarchical approximation based on finite elements and meshless methods is presented, which couples regions where finite elements or meshless method are used to interpolate: continuity and consistency is preserved.
References
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Journal ArticleDOI
Adaptivity based on error estimation for viscoplastic softening materials
TL;DR: Adapt strategies are found to be essential to detect the collapse mechanism and to assess the optimal location of the elements in the mesh to deal with highly non-linear material model.
Journal ArticleDOI
Theoretical formulations for adaptive finite element computations
TL;DR: The present adaptive mesh refinement strategy significantly improves adaptivity performance and has higher error convergence rates than those usually used.
On the simulation of thermo-mechanical forming processes
TL;DR: In this article, a formulation for elastic-plastic constitutive equations is given based on principles of continuum thermo-mechanics and thermodynamics, and a mixed Eulerian-Lagrangian finite element method is developed by which nodal point locations may be adapted independently of material displacement.
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