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Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities

โœ Scribed by Zi Cai Li (auth.)

Publisher
Springer US
Year
1998
Tongue
English
Leaves
488
Series
Mathematics and Its Applications 444
Edition
1
Category
Library
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โœฆ Synopsis

In this book the author sets out to answer two important questions: 1. Which numerical methods may be combined together? 2. How can different numerical methods be matched together? In doing so the author presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM, RGM-FDM, etc. The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed. The author provides the matching rules so that optimal convergence, even superconvergence, and optimal stability can be achieved, and also warns of the matching pitfalls to avoid.
Audience: The book is intended for both mathematicians and engineers and may be used as text for advanced students.

โœฆ Table of Contents

Front Matter....Pages i-xxiv
Front Matter....Pages 1-1
Different Numerical Methods....Pages 5-48
Singularities and Treatments....Pages 49-97
Front Matter....Pages 99-99
Boundary Approximation Methods....Pages 103-137
Combinations of RGM and FEM....Pages 139-174
Combinations of Various Fems....Pages 175-204
Front Matter....Pages 205-205
Lagrange Multipliers and Other Coupling Techniques....Pages 209-224
Penalty Techniques....Pages 225-249
Simplified Hybrid Methods....Pages 251-280
Penalty Plus Hybrid Techniques....Pages 281-308
Optimal Combinations for Various Fems....Pages 309-326
Combinations of RGM and FDM....Pages 327-348
Front Matter....Pages 349-349
Crack-Infinity Problem....Pages 353-367
Wind Flow Over Buildings....Pages 369-381
Global Superconvergence in Combinations....Pages 383-397
Iterative Substructing Methods....Pages 399-422
Schwarz Alternating Method....Pages 423-442
Epilogue....Pages 443-444
Back Matter....Pages 445-478

โœฆ Subjects

Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering

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