| Description |
1 online resource (xi, 282 pages) : illustrations |
| Series |
Lecture notes in computational science and engineering, 1439-7358 ; 85 |
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Lecture notes in computational science and engineering ; 85.
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| Contents |
""Frontiers in Numerical Analysis -- Durham 2010""; ""Preface""; ""Acknowledgements""; ""Contents""; ""Contributors""; ""Some Remarks on Eigenvalue Approximation by Finite Elements""; ""1 Introduction""; ""2 Variationally Posed Eigenvalue Problems""; ""3 One Dimensional Examples""; ""3.1 Standard Laplace Eigenvalue Problem""; ""3.2 Laplace Eigenvalue Problem in Mixed Form""; ""4 Eigenvalue Problems in Mixed Form""; ""4.1 Inf-Sup Conditions""; ""4.2 Convergence of Eigenvalue Problems in Mixed Forms""; ""5 Error Estimates for Multiple Eigenvalues"" |
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""5.1 Fundamental Results on Spectral Approximation""""5.2 Error Estimates for Ritz-Galerkin Approximation of Multiple Eigenvalues""; ""5.3 Numerical Results""; ""6 A Posteriori Error Analysis""; ""6.1 Some Introductory Remarks""; ""6.2 A Posteriori Error Estimators""; ""6.3 Standard Finite Element Approximation""; ""6.4 Mixed Finite Element Approximation""; ""6.4.1 A Posteriori Error Analysis for Brezzi�Douglas�Marini Finite Elements""; ""6.4.2 A Posteriori Error Analysis for Raviart-Thomas Finite Elements""; ""6.5 Numerical Results""; ""References""; ""C0 Interior Penalty Methods"" |
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""1 Introduction""""1.1 Basic Notations and Definitions""; ""2 Model Problems""; ""2.1 Weak Formulations""; ""2.2 Elliptic Regularity""; ""2.3 Ramifications of Elliptic Regularity""; ""C0 Interior Penalty Methods""; ""3.1 Well-Posedness of the Discrete Problems""; ""3.2 Galerkin Orthogonality""; ""3.3 A Standard Error Analysis""; ""3.4 Complications""; ""3.5 An Alternative Expression for the Discrete Bilinear Form""; ""3.6 Conditioning""; ""4 Enriching Operators""; ""4.1 Enriching Operator Based on the Hsieh-Clough-Tocher Macro Element""; ""4.2 Enriching Operator Based on C1 Relatives"" |
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""7.1 An A Posteriori Error Estimator""""7.2 Reliability""; ""7.3 Efficiency""; ""7.4 Adaptive Algorithms""; ""8 Multigrid Methods""; ""8.1 Set-Up""; ""8.2 Intergrid Transfer Operators and Smoothers""; ""8.2.1 A Standard Smoother""; ""8.2.2 A Nonstandard Smoother""; ""8.3 Multigrid Algorithms""; ""8.3.1 V-Cycle Algorithm""; ""8.3.2 W-Cycle Algorithm""; ""8.3.3 F-Cycle Algorithm""; ""8.4 Convergence Analysis""; ""8.4.1 Recurrence Relations for Error Propagation Operators""; ""8.4.2 Mesh-Dependent Norms and Smoothing Properties"" |
| Summary |
Annotation This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences |
| Analysis |
Computer science -- Mathematics |
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Computational Mathematics and Numerical Analysis |
| Bibliography |
Includes bibliographical references |
| Subject |
Numerical analysis -- Congresses
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Mathematics.
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Mathematics
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mathematics.
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applied mathematics.
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Análisis numérico -- Congresos
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Matemáticas
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Mathematics
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Numerical analysis
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| Genre/Form |
proceedings (reports)
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Conference papers and proceedings
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Conference papers and proceedings.
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Actes de congrès.
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| Form |
Electronic book
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| Author |
Blowey, James F.
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Jensen, Max.
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LMS-EPSRC Computational Mathematics and Scientific Computing Summer School (12th : 2010 : Durham, England)
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| LC no. |
2011944196 |
| ISBN |
9783642239144 |
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3642239145 |
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3642239137 |
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9783642239137 |
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