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図書

図書
Mark Ainsworth and J. Tinsley Oden
出版情報: New York : John Wiley & Sons, c2000  xvii, 240 p. ; 25 cm
シリーズ名: Pure and applied mathematics
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Preface
Acknowledgments
Introduction / 1:
A Posteriori Error Estimation: The Setting / 1.1:
Status and Scope / 1.2:
Finite Element Nomenclature / 1.3:
Sobolev Spaces / 1.3.1:
Inverse Estimates / 1.3.2:
Finite Element Partitions / 1.3.3:
Finite Element Spaces on Triangles / 1.3.4:
Finite Element Spaces on Quadrilaterals / 1.3.5:
Properties of Lagrange Basis Functions / 1.3.6:
Finite Element Interpolation / 1.3.7:
Patches of Elements / 1.3.8:
Regularized Approximation Operators / 1.3.9:
Model Problem / 1.4:
Properties of A Posteriori Error Estimators / 1.5:
Bibliographical Remarks / 1.6:
Explicit A Posteriori Estimators / 2:
A Simple A Posteriori Error Estimate / 2.1:
Efficiency of Estimator / 2.3:
Bubble Functions / 2.3.1:
Bounds on the Residuals / 2.3.2:
Proof of Two-Sided Bounds on the Error / 2.3.3:
A Simple Explicit Least Squares Error Estimator / 2.4:
Estimates for the Pointwise Error / 2.5:
Regularized Point Load / 2.5.1:
Regularized Green's Function / 2.5.2:
Two-Sided Bounds on the Pointwise Error / 2.5.3:
Implicit A Posteriori Estimators / 2.6:
The Subdomain Residual Method / 3.1:
Formulation of Subdomain Residual Problem / 3.2.1:
Preliminaries / 3.2.2:
Equivalence of Estimator / 3.2.3:
Treatment of Residual Problems / 3.2.4:
The Element Residual Method / 3.3:
Formulation of Local Residual Problem / 3.3.1:
Solvability of the Local Problems / 3.3.2:
The Classical Element Residual Method / 3.3.3:
Relationship with Explicit Error Estimators / 3.3.4:
Efficiency and Reliability of the Estimator / 3.3.5:
The Influence and Selection of Subspaces / 3.4:
Exact Solution of Element Residual Problem / 3.4.1:
Analysis and Selection of Approximate Subspaces / 3.4.2:
Conclusions / 3.4.3:
Recovery-Based Error Estimators / 3.5:
Examples of Recovery-Based Estimators / 4.1:
An Error Estimator for a Model Problem in One Dimension / 4.1.1:
An Error Estimator for Bilinear Finite Element Approximation / 4.1.2:
Recovery Operators / 4.2:
Approximation Properties of Recovery Operators / 4.2.1:
The Superconvergence Property / 4.3:
Application to A Posteriori Error Estimation / 4.4:
Construction of Recovery Operators / 4.5:
The Zienkiewicz-Zhu Patch Recovery Technique / 4.6:
Linear Approximation on Triangular Elements / 4.6.1:
Quadratic Approximation on Triangular Elements / 4.6.2:
Patch Recovery for Quadrilateral Elements / 4.6.3:
A Cautionary Tale / 4.7:
Estimators, Indicators, and Hierarchic Bases / 4.8:
Saturation Assumption / 5.1:
Analysis of Estimator / 5.3:
Error Estimation Using a Reduced Subspace / 5.4:
The Strengthened Cauchy-Schwarz Inequality / 5.5:
Examples / 5.6:
Multilevel Error Indicators / 5.7:
The Equilibrated Residual Method / 5.8:
The Equilibrated Flux Conditions / 6.1:
Equilibrated Fluxes on Regular Partitions / 6.4:
First-Order Equilibration Condition / 6.4.1:
The Form of the Boundary Fluxes / 6.4.2:
Equilibration Conditions in Terms of the Moments / 6.4.3:
Local Patch Problems for the Flux Moments / 6.4.4:
Procedure for Resolution of Patch Problems / 6.4.5:
Summary / 6.4.6:
Efficiency of the Estimator / 6.5:
Stability of the Equilibrated Fluxes / 6.5.1:
Proof of Efficiency of the Estimator / 6.5.2:
Equilibrated Fluxes on Partitions Containing Hanging Nodes / 6.6:
First-Order Equilibration / 6.6.1:
Flux Moments for Unconstrained Nodes / 6.6.2:
Flux Moments with Respect to Constrained Nodes / 6.6.3:
Recovery of Actual Fluxes / 6.6.4:
Equilibrated Fluxes for Higher-Order Elements / 6.7:
Determination of the Flux Moments / 6.7.1:
Methodology for the Comparison of Estimators / 6.8:
Overview of the Technique / 7.1:
Approximation over an Interior Subdomain / 7.3:
Translation Invariant Meshes / 7.3.1:
Lower Bounds on the Error / 7.3.2:
Interior Estimates / 7.3.3:
Asymptotic Finite Element Approximation / 7.4:
Periodic Finite Element Projection on Reference Cell / 7.4.1:
Periodic Finite Element Projection on a Physical Cell / 7.4.2:
Periodic Extension on a Subdomain / 7.4.3:
Stability of Estimators / 7.4.4:
Verification of Stability Condition for Explicit Estimator / 7.5.1:
Verification of Stability Condition for Implicit Estimators / 7.5.2:
Verification of Stability Condition for Recovery-Based Estimator / 7.5.3:
Elementary Consequences of the Stability Condition / 7.5.4:
Evaluation of Effectivity Index in the Asymptotic Limit / 7.5.5:
An Application of the Theory / 7.6:
Computation of Asymptotic Finite Element Solution / 7.6.1:
Evaluation of the Error in Asymptotic Finite Element Approximation / 7.6.2:
Computation of Limits on the Asymptotic Effectivity Index for Zienkiewicz-Zhu Patch Recovery Estimator / 7.6.3:
Application to Equilibrated Residual Method / 7.6.4:
Application to Implicit Element Residual Method / 7.6.5:
Estimation of the Errors in Quantities of Interest / 7.7:
Estimates for the Error in Quantities of Interest / 8.1:
Upper and Lower Bounds on the Errors / 8.3:
Goal-Oriented Adaptive Refinement / 8.4:
Example of Goal-Oriented Adaptivity / 8.5:
Adaptivity Based on Control of Global Error in Energy / 8.5.1:
Goal-Oriented Adaptivity Based on Pointwise Quantities of Interest / 8.5.2:
Local and Pollution Errors / 8.6:
Some Extensions / 8.7:
Stokes and Oseen's Equations / 9.1:
A Posteriori Error Analysis / 9.2.1:
Incompressible Navier-Stokes Equations / 9.2.2:
Extensions to Nonlinear Problems / 9.4:
A Class of Nonlinear Problems / 9.4.1:
A Posteriori Error Estimation / 9.4.2:
Estimation of the Residual / 9.4.3:
References / 9.5:
Index
Preface
Acknowledgments
Introduction / 1:
2.

図書

図書
edited by the Organizing committee, J.T. Oden ... [et al.]
出版情報: Austin : The Texas Institute for Computational Mechanics, c1974  xvii, 1010 p. ; 24 cm
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3.

図書

図書
editors, Ahmed K. Noor, J. Tinsley Oden
出版情報: New York, NY : American Society of Mechanical Engineers, c1989  xiv, 556 p. ; 27 cm
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4.

図書

図書
J.T. Oden, J.N. Reddy
出版情報: New York : Wiley, c1976  xii, 429 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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5.

図書

図書
edited by R.H. Gallagher ... [et al.]
出版情報: London : John Wiley & Sons, c1975  xiv, 290 p. ; 24 cm.
シリーズ名: Finite elements in fluids / edited by R.H. Gallagher ... [et al.] ; v. 1
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6.

図書

図書
edited by R.H. Gallagher ... [et al.]
出版情報: London : John Wiley & Sons, c1975  xii, 287 p. ; 24 cm.
シリーズ名: Finite elements in fluids / edited by R.H. Gallagher ... [et al.] ; v. 2
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7.

図書

図書
edited by Klaus-Jürgen Bathe, J. Tinsley Oden, and Walter Wunderlich
出版情報: [Cambridge] : Massachusetts Institute of Technology, c1977  xvi, 1091 p. ; 24 cm
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8.

図書

図書
[by] J.T. Oden
出版情報: New York : McGraw-Hill, 1972  xv, 432 p. ; 24 cm
シリーズ名: Advanced engineering series
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9.

図書

図書
edited by J.T. Oden and E.R.A. Oliveira
出版情報: [Huntsville] : [University of Alabama in Huntsville Press], c1973  xi, 561 p. ; 26 cm
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10.

図書

図書
edited by J.T. Oden
出版情報: Amsterdam ; New York : North-Holland Pub. Co. , New York : sole distributors for the U.S.A. and Canada, Elsevier North-Holland, 1980  viii, 539 p. ; 23 cm
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