Advances in Adaptive Computational Methods in Mechanics

P. Ladevèze and J.T. Oden (Eds.)9780080433271, 9780080525938, 0080433278

Mastering modelling, and in particular numerical models, is becoming a crucial and central question in modern computational mechanics. Various tools, able to quantify the quality of a model with regard to another one taken as the reference, have been derived. Applied to computational strategies, these tools lead to new computational methods which are called “adaptive”. The present book is concerned with outlining the state of the art and the latest advances in both these important areas.
Papers are selected from a Workshop (Cachan 17-19 September 1997) which is the third of a series devoted to Error Estimators and Adaptivity in Computational Mechanics. The Cachan Workshop dealt with latest advances in adaptive computational methods in mechanics and their impacts on solving engineering problems. It was centered too on providing answers to simple questions such as: what is being used or can be used at present to solve engineering problems? What should be the state of art in the year 2000? What are the new questions involving error estimators and their applications?

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Table of contents :
Content:
Preface
Page v
P. Ladevèze, J.T. Oden

Recovery procedures in error estimation and adaptivity: Adaptivity in linear problems Original Research Article
Pages 3-23
O.C. Zienkiewicz, B. Boroomand, J.Z. Zhu

The relationship of some a posteriori error estimators Original Research Article
Pages 25-42
J.Z. Zhu, Zhimin Zhang

A technique for a posteriori error estimation of h-p approximations of the Stokes equations Original Research Article
Pages 43-63
J.T. Oden, S. Prudhomme

A mathematical framework for the P. Ladevèze a posteriori error bounds in finite element methods Original Research Article
Pages 65-78
Ph. Destuynder, M. Collot, M. Salaün

Adaptive finite elements in elastoplasticity with mechanical error indicators and Neumann-type estimators Original Research Article
Pages 81-99
E. Stein, F.J. Barthold, S. Ohnimus, M. Schmidt

A reliable a posteriori error estimator for adaptive hierarchic modelling Original Research Article
Pages 101-114
M. Ainsworth, M. Arnold

A two-scale strategy and a posteriori error estimation for modeling heterogeneous structures Original Research Article
Pages 115-133
Nicolas Moës, J. Tinsley Oden, Kumar Vemaganti

A modelling error estimator for dynamic structural model updating Original Research Article
Pages 135-151
P. Ladevèze

A-posteriori estimation of the error in the error estimate Original Research Article
Pages 155-197
I. Babuska, T. Strouboulis, S.K. Gangaraj, K. Copps, D.K. Datta

Bounds for linear-functional outputs of coercive partial differential equations: Local indicators and adaptive refinement Original Research Article
Pages 199-216
J. Peraire, A.T. Patera

On adaptivity and error criteria for meshfree methods Original Research Article
Pages 217-228
Ted Belytschko, Wing Kam Liu, Mike Singer

A posteriori constitutive relation error estimators for nonlinear finite element analysis and adaptive control Original Research Article
Pages 231-256
Pierre Ladevèze, Nicolas Moës

A review of a posteriori error estimation techniques for elasticity problems Review Article
Pages 257-274
R. Verfürth

A posteriori error control and mesh adaptation for FE models in elasticity and elasto-plasticity Original Research Article
Pages 275-292
R. Rannacher, F.T. Suttmeier

An adaptive finite element approach in associated and non-associated plasticity considering localization phenomena Original Research Article
Pages 293-308
W. Wunderlich, H. Cramer, G. Steinl

An alpha-adaptive approach for stabilized finite element solution of advective-diffusive problems with sharp gradients Original Research Article
Pages 309-323
E. Oñate, J. García, S. Idelsohn

Adaptive strategy for transient/coupled problems: Applications to thermoelasticity and elastodynamics Original Research Article
Pages 325-332
D. Aubry, D. Lucas, B. Tie

Error estimation and adaptive finite element analysis of softening solids Original Research Article
Pages 333-347
Antonio Huerta, Pedro Díez, Antonio Rodríguez-Ferran, Gilles Pijaudier-Cabot

Aspects of adaptive strategies for large deformation problems at finite inelastic strains Original Research Article
Pages 349-363
D. Perić, M. Dutko, D.R.J. Owen

Adaptive solutions in industrial forming process simulation Original Research Article
Pages 365-381
T. Coupez, L. Fourment, J.L. Chenot

Recovery procedures in error estimation and adaptivity: Adaptivity in non-linear problems of elasto-plasticity behaviour Original Research Article
Pages 383-410
B. Boroomand, O.C. Zienkiewicz

3-D error estimation and mesh adaptation using improved R.E.P. method Original Research Article
Pages 413-426
Pierre Beckers, Emilio Dufeu

Adaptive methods and related issues from the viewpoint of hybrid equilibrium finite element models Original Research Article
Pages 427-441
O.J.B. Almeida Pereira, J.P. Moitinho de Almeida, E.A.W. Maunder

Error estimator and adaptivity for three-dimensional finite element analyses Original Research Article
Pages 443-457
P. Coorevits, J.-P. Dumeau, J.-P. Pelle

Error estimation and adaptivity for h-version eigenfrequency analysis Original Research Article
Pages 461-475
Nils-Erik Wiberg, Patrik Hager

Error estimation and adaptivity for the finite element method in acoustics Original Research Article
Pages 477-492
Ph. Bouillard, F. Ihlenburg

Error through the constitutive relation for beam or C° plate finite elements: static and vibration analyses Original Research Article
Pages 493-512
P. Boisse, G. Coffignal

A posteriori error analysis for steady-state Maxwell’s equations Original Research Article
Pages 513-526
L. Demkowicz

Author index
Pages 527-528