A Posteriori Error Estimation in Finite Element AnalysisAn up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on aposteriori error estimation for finite element approximation inmechanics and mathematics. It emphasizes methods for ellipticboundary value problems and includes applications to incompressibleflow and nonlinear problems. Recent years have seen an explosion in the study of a posteriorierror estimators due to their remarkable influence on improvingboth accuracy and reliability in scientific computing. In an effortto provide an accessible source, the authors have sought to presentkey ideas and common principles on a sound mathematicalfooting. Topics covered in this timely reference include: * Implicit and explicit a posteriori error estimators * Recovery-based error estimators * Estimators, indicators, and hierarchic bases * The equilibrated residual method * Methodology for the comparison of estimators * Estimation of errors in quantities of interest A Posteriori Error Estimation in Finite Element Analysis is a lucidand convenient resource for researchers in almost any field offinite element methods, and for applied mathematicians andengineers who have an interest in error estimation and/or finiteelements. |
Contents
Introduction 17245 | 1 |
Explicit A Posteriori Estimators | 20 |
Implicit A Posteriori Estimators | 43 |
RecoveryBased Error Estimators | 68 |
Approximation Properties of Recovery | 73 |
Estimators Indicators and Hierarchic Bases | 85 |
59 | 99 |
The Equilibrated Residual Method | 112 |
Other editions - View all
A Posteriori Error Estimation in Finite Element Analysis Mark Ainsworth,J. Tinsley Oden Limited preview - 2011 |
Common terms and phrases
adaptive refinement analysis applying approximation properties asymptotic finite element B(ux Babuška basis functions bilinear form boundary fluxes boundary value problem bubble functions Cauchy-Schwarz inequality cell C(ca Chº computation consists constructed defined denote domain edge effectivity index eigenvalues energy norm Engrg equation equilibration conditions exists a constant finite element approximation finite element method finite element subspace finite-dimensional first-order flux moments Galerkin approximation H¹,per independent of h inner product interpolant Lagrange basis Lemma linear functional matrix mesh N₁ nodes Numer obtained patch recovery periodic finite element piecewise linear polynomial positive constant posteriori error estimation procedure Proof quadratic quadrilateral elements quantity of interest recovered gradient recovery operator reference cell result shown in Figure strengthened Cauchy-Schwarz inequality subdomain superconvergence Theorem tion triangle inequality triangular elements true error true solution vanishes vertex Xper дих дпк КЕР
References to this book
The Mathematical Theory of Finite Element Methods Susanne Brenner,L. Ridgway Scott Limited preview - 2002 |
Finite Elemente: Theorie, schnelle Löser und Anwendungen in der ... Dietrich Braess No preview available - 2007 |