A posteriori error estimation in finite element analysis / / Mark Ainsworth and J. Tinsley Oden

• Autore: Ainsworth Mark <1965->
• Pubblicazione: New York, New York : , : John Wiley & Sons, Inc., , 2000; ©2000
• Descrizione fisica: 1 online resource (266 p.)
• Disciplina: 620.001; 620.00151535
• Soggetto topico: Finite element method; Error analysis (Mathematics)
• Persona (resp. second.): OdenJ. Tinsley (John Tinsley) <1936->
• Note generali: "A Wiley-Interscience Publication."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: A Posteriori Error Estimation in Finite Element Analysis; Contents; Preface; Acknowledgments; 1 Introduction; 1.1 A Posteriori Error Estimation: The Setting; 1.2 Status and Scope; 1.3 Finite Element Nomenclature; 1.3.1 Sobolev Spaces; 1.3.2 Inverse Estimates; 1.3.3 Finite Element Partitions; 1.3.4 Finite Element Spaces on Triangles; 1.3.5 Finite Element Spaces on Quadrilaterals; 1.3.6 Properties of Lagrange Basis Functions; 1.3.7 Finite Element Interpolation; 1.3.8 Patches of Elements; 1.3.9 Regularized Approximation Operators; 1.4 Model Problem ; 1.5 Properties of A Posteriori Error Estimators1.6 Bibliographical Remarks; 2 Explicit A Posteriori Estimators; 2.1 Introduction; 2.2 A Simple A Posteriori Error Estimate; 2.3 Efficiency of Estimator; 2.3.1 Bubble Functions; 2.3.2 Bounds on the Residuals; 2.3.3 Proof of Two-Sided Bounds on the Error; 2.4 A Simple Explicit Least Squares Error Estimator; 2.5 Estimates for the Pointwise Error; 2.5.1 Regularized Point Load; 2.5.2 Regularized Green's Function; 2.5.3 Two-Sided Bounds on the Pointwise Error; 2.6 Bibliographical Remarks; 3 Implicit A Posteriori Estimators; 3.1 Introduction ; 3.2 The Subdomain Residual Method3.2.1 Formulation of Subdomain Residual Problem; 3.2.2 Preliminaries; 3.2.3 Equivalence of Estimator; 3.2.4 Treatment of Residual Problems; 3.3 The Element Residual Method; 3.3.1 Formulation of Local Residual Problem; 3.3.2 Solvability of the Local Problems; 3.3.3 The Classical Element Residual Method; 3.3.4 Relationship with Explicit Error Estimators; 3.3.5 Efficiency and Reliability of the Estimator; 3.4 The Influence and Selection of Subspaces; 3.4.1 Exact Solution of Element Residual Problem; 3.4.2 Analysis and Selection of Approximate Subspaces ; 3.4.3 Conclusions3.5 Bibliographical Remarks; 4 Recovery-Based Error Estimators; 4.1 Examples of Recovery-Based Estimators; 4.1.1 An Error Estimator for a Model Problem in One Dimension; 4.1.2 An Error Estimator for Bilinear Finite Element Approximation; 4.2 Recovery Operators; 4.2.1 Approximation Properties of Recovery Operators; 4.3 The Superconvergence Property; 4.4 Application to A Posteriori Error Estimation; 4.5 Construction of Recovery Operators; 4.6 The Zienkiewicz-Zhu Patch Recovery Technique; 4.6.1 Linear Approximation on Triangular Elements ; 4.6.2 Quadratic Approximation on Triangular Elements4.6.3 Patch Recovery for Quadrilateral Elements; 4.7 A Cautionary Tale; 4.8 Bibliographical Remarks; 5 Estimators, Indicators, and Hierarchic Bases; 5.1 Introduction; 5.2 Saturation Assumption; 5.3 Analysis of Estimator; 5.4 Error Estimation Using a Reduced Subspace; 5.5 The Strengthened Cauchy-Schwarz Inequality; 5.6 Examples; 5.7 Multilevel Error Indicators; 5.8 Bibliographical Remarks; 6 The Equilibrated Residual Method; 6.1 Introduction; 6.2 The Equilibrated Residual Method; 6.3 The Equilibrated Flux Conditions ; 6.4 Equilibrated Fluxes on Regular Partitions
• Sommario/riassunto: An up-to-date, one-stop reference-complete with applicationsThis 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 sour
• Titolo autorizzato: A posteriori error estimation in finite element analysis
• ISBN: 1-283-28259-3; 9786613282590; 1-118-03107-5; 1-118-03282-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910829852103321
• Lo trovi qui: Univ. Federico II
• Serie: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts