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Informationen zum Autor MARK AINSWORTH, PhD, is Professor of Applied Mathematics atStrathclyde University, UK. J. TINSLEY ODEN, PhD, is Director of the Texas Institute forComputational and Applied Mathematics at the University of Texas,Austin. Klappentext An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on a posteriori error estimation for finite element approximation in mechanics and mathematics. It emphasizes methods for elliptic boundary value problems and includes applications to incompressible flow and nonlinear problems. Recent years have seen an explosion in the study of a posteriori error estimators due to their remarkable influence on improving both accuracy and reliability in scientific computing. In an effort to provide an accessible source, the authors have sought to present key ideas and common principles on a sound mathematical footing. 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 lucid and convenient resource for researchers in almost any field of finite element methods, and for applied mathematicians and engineers who have an interest in error estimation and/or finite elements. Zusammenfassung A posteriori error estimators have been intensely studied in recent years! owing to their remarkable capacity to enhance both speed and accuracy in computing. By effectively estimating error! the door has been opened for the possibility of controlling the entire computational process through new adaptive algorithms. Inhaltsverzeichnis Preface xiii Acknowledgments xvii 1 Introduction 1 1.1 A Posteriori Error Estimation: The Setting 1 1.2 Status and Scope 2 1.3 Finite Element Nomenclature 4 1.3.1 Sobolev Spaces 5 1.3.2 Inverse Estimates 7 1.3.3 Finite Element Partitions 9 1.3.4 Finite Element Spaces on Triangles 10 1.3.5 Finite Element Spaces on Quadrilaterals 11 1.3.6 Properties of Lagrange Basis Functions 12 1.3.7 Finite Element Interpolation 12 1.3.8 Patches of Elements 13 1.3.9 Regularized Approximation Operators 14 1.4 Model Problem 15 1.5 Properties of A Posteriori Error Estimators 16 1.6 Bibliographical Remarks 18 2 Explicit A Posteriori Estimators 19 2.1 Introduction 19 2.2 A Simple A Posteriori Error Estimate 20 2.3 Efficiency of Estimator 23 2.3.1 Bubble Functions 23 2.3.2 Bounds on the Residuals 28 2.3.3 Proof of Two-Sided Bounds on the Error 31 2.4 A Simple Explicit Least Squares Error Estimator 32 2.5 Estimates for the Pointwise Error 34 2.5.1 Regularized Point Load 35 2.5.2 Regularized Green's Function 38 2.5.3 Two-Sided Bounds on the Pointwise Error 39 2.6 Bibliographical Remarks 4% 3 Implicit A Posteriori Estimators 43 3.1 Introduction 43 3.2 The Subdomain Residual Method 44 3.2.1 Formulation of Subdomain Residual Problem 45 3.2.2 Preliminaries 46 3.2.3 Equivalence of Estimator ^7 3.2.4 Treatment of Residual Problems 49 3.3 The Element Residual Method 50 3.3.1 Formulation of Local Residual Problem 50 3.3.2 Solvability of the Local Problems 52 3.3.3 The Classical Element Residual Method 54 3.3.4 Relationship with Explicit Error Estimators 54 3.3.5 Efficiency and Reliability of the Estimator 55 3.4 The Influence and Selection of Subspaces 56 3.4.1 Exact Solution of Element Residual Prob...
