LEADER 05472nam 2200661 450 001 9910829852103321 005 20230422033033.0 010 $a1-283-28259-3 010 $a9786613282590 010 $a1-118-03107-5 010 $a1-118-03282-9 035 $a(CKB)3460000000080819 035 $a(EBL)694898 035 $a(SSID)ssj0000555332 035 $a(PQKBManifestationID)11359233 035 $a(PQKBTitleCode)TC0000555332 035 $a(PQKBWorkID)10519154 035 $a(PQKB)11094489 035 $a(MiAaPQ)EBC694898 035 $a(OCoLC)761321857 035 $a(EXLCZ)993460000000080819 100 $a20160816h20002000 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA posteriori error estimation in finite element analysis /$fMark Ainsworth and J. Tinsley Oden 210 1$aNew York, New York :$cJohn Wiley & Sons, Inc.,$d2000. 210 4$dİ2000 215 $a1 online resource (266 p.) 225 0 $aPure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts 300 $a"A Wiley-Interscience Publication." 311 $a0-471-29411-X 320 $aIncludes bibliographical references and index. 327 $aA 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 327 $a1.5 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 327 $a3.2 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 327 $a3.4.3 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 327 $a4.6.2 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 327 $a6.4 Equilibrated Fluxes on Regular Partitions 330 $aAn up-to-date, one-stop reference-complete with applicationsThis volume presents the most up-to-date information available on a posteriori error estimation for finite element approximation in mechanics and mathematics. It emphasizes methods for elliptic boundary value problems and includes applications to incompressible flow and nonlinear problems.Recent years have seen an explosion in the study of a posteriori error estimators due to their remarkable influence on improving both accuracy and reliability in scientific computing. In an effort to provide an accessible sour 410 0$aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 606 $aFinite element method 606 $aError analysis (Mathematics) 615 0$aFinite element method. 615 0$aError analysis (Mathematics) 676 $a620.001 676 $a620.00151535 700 $aAinsworth$b Mark$f1965-$01670875 702 $aOden$b J. Tinsley (John Tinsley)$f1936- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910829852103321 996 $aA posteriori error estimation in finite element analysis$94033025 997 $aUNINA