Advances In Adaptive Computational Methods In Mechanics
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.\...
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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?
PrefaceRecovery procedures in error estimation and adaptivity: Adaptivity in linear problems3The relationship of some a posteriori error estimators25A technique for a posteriori error estimation of h-p approximations of the Stokes equations43A mathematical framework for the P. Ladeveze a posteriori error bounds in finite element methods65Adaptive finite element in elastoplasticity with mechanical error indicators and Neumann-type estimators81A reliable a posteriori error estimator for adaptive hierarchic modelling101A two-scale strategy and a posteriori error estimation for modelling heterogeneous structures115A modelling error estimator for dynamic structural model updating135A posteriori estimation of the error in the error estimate155Bounds for linear-functional outputs of coercive partial differential equations: Local indicators and adaptive refinement199On adaptivity and error criteria in meshfree methods217A posteriori constitutive relation error estimators for nonlinear finite element analysis and adaptive control231A review of a posteriori error estimation techniques for elasticity problems257A posteriori error control and mesh adaptation for F.E. models in elasticity and elastoplasticity275An adaptive finite element approach in associated and non-associated plasticity considering localization phenomena293An [alpha]-adaptivity approach for advective-diffusive and fluid flow problems309Adaptive strategy for transient/coupled problems. Applications to thermoelasticity and elastodynamics325Error estimation and adaptive finite element analysis of softening solids333Aspects of adaptive strategies for large deformation problems at finite inelastic strains349Adaptive solutions in industrial forming process simulation365Recovery procedures in error estimation and adaptivity: Adaptivity in non-linear problems of elasto-plasticity behaviour3833-D error estimation and mesh adaptation using improved R.E.P. method413Adaptive methods and related issues from the viewpoint of hybrid equilibrium finite element models427Error estimator and adaptivity for three-dimensional finite element analyses443Error estimation and adaptivity for h-version eigenfrequency analysis461Error estimation and adaptivity for the finite element method in acoustics477Error through the constitutive relation for beam or [actual symbol not reproducible] plate finite element: Static and vibration analyses493A posteriori error analysis for steady-state Maxwell's equation513Author Index527
