1.

Record Nr.

UNINA9911019991303321

Autore

Lui S. H (Shaun H.), <1961->

Titolo

Numerical analysis of partial differential equations / / S.H. Lui

Pubbl/distr/stampa

Hoboken, N.J., : Wiley, c2011

ISBN

9786613282774

9781283282772

1283282771

9781118111116

1118111117

9781118111130

1118111133

9781118111109

1118111109

Descrizione fisica

1 online resource (508 p.)

Collana

Pure and applied mathematics : a Wiley series of texts, monographs, and tracts

Classificazione

MAT034000

Disciplina

518.64

518/.64

Soggetti

Differential equations, Partial - Numerical solutions

Variational inequalities (Mathematics)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Numerical Analysis of Partial Differential Equations; Contents; Preface; Acknowledgments; 1 Finite Difference; 1.1 Second-Order Approximation for Δ; 1.2 Fourth-Order Approximation for Δ; 1.3 Neumann Boundary Condition; 1.4 Polar Coordinates; 1.5 Curved Boundary; 1.6 Difference Approximation for Δ2; 1.7 A Convection-Diffusion Equation; 1.8 Appendix: Analysis of Discrete Operators; 1.9 Summary and Exercises; 2 Mathematical Theory of Elliptic PDEs; 2.1 Function Spaces; 2.2 Derivatives; 2.3 Sobolev Spaces; 2.4 Sobolev Embedding Theory; 2.5 Traces; 2.6 Negative Sobolev Spaces

2.7 Some Inequalities and Identities2.8 Weak Solutions; 2.9 Linear Elliptic PDEs; 2.10 Appendix: Some Definitions and Theorems; 2.11 Summary and Exercises; 3 Finite Elements; 3.1 Approximate Methods of



Solution; 3.2 Finite Elements in 1D; 3.3 Finite Elements in 2D; 3.4 Inverse Estimate; 3.5 L2 and Negative-Norm Estimates; 3.6 Higher-Order Elements; 3.7 A Posteriori Estimate; 3.8 Quadrilateral Elements; 3.9 Numerical Integration; 3.10 Stokes Problem; 3.11 Linear Elasticity; 3.12 Summary and Exercises; 4 Numerical Linear Algebra; 4.1 Condition Number; 4.2 Classical Iterative Methods

4.3 Krylov Subspace Methods4.4 Direct Methods; 4.5 Preconditioning; 4.6 Appendix: Chebyshev Polynomials; 4.7 Summary and Exercises; 5 Spectral Methods; 5.1 Trigonometric Polynomials; 5.2 Fourier Spectral Method; 5.3 Orthogonal Polynomials; 5.4 Spectral Galerkin and Spectral Tau Methods; 5.5 Spectral Collocation; 5.6 Polar Coordinates; 5.7 Neumann Problems; 5.8 Fourth-Order PDEs; 5.9 Summary and Exercises; 6 Evolutionary PDEs; 6.1 Finite Difference Schemes for Heat Equation; 6.2 Other Time Discretization Schemes; 6.3 Convection-Dominated equations; 6.4 Finite Element Scheme for Heat Equation

6.5 Spectral Collocation for Heat Equation6.6 Finite Difference Scheme for Wave Equation; 6.7 Dispersion; 6.8 Summary and Exercises; 7 Multigrid; 7.1 Introduction; 7.2 Two-Grid Method; 7.3 Practical Multigrid Algorithms; 7.4 Finite Element Multigrid; 7.5 Summary and Exercises; 8 Domain Decomposition; 8.1 Overlapping Schwarz Methods; 8.2 Orthogonal Projections; 8.3 Non-overlapping Schwarz Method; 8.4 Substructuring Methods; 8.5 Optimal Substructuring Methods; 8.6 Summary and Exercises; 9 Infinite Domains; 9.1 Absorbing Boundary Conditions; 9.2 Dirichlet-Neumann Map; 9.3 Perfectly Matched Layer

9.4 Boundary Integral Methods9.5 Fast Multipole Method; 9.6 Summary and Exercises; 10 Nonlinear Problems; 10.1 Newton's Method; 10.2 Other Methods; 10.3 Some Nonlinear Problems; 10.4 Software; 10.5 Program Verification; 10.6 Summary and Exercises; Answers to Selected Exercises; References; Index

Sommario/riassunto

A balanced guide to the essential techniques for solving elliptic partial differential equations  Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the num