OXFORD UNIVERSITY PRESS

Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

ISBN : 9780199577040

参考価格(税込): 
¥22,825
著者: 
Klaus Boehmer
ページ
776 ページ
フォーマット
Hardcover
サイズ
178 x 253 mm
刊行日
2010年10月
シリーズ
Numerical Mathematics and Scientific Computation
メール送信
印刷

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, creating an exciting interplay between the subjects. This is the first and only book to prove in a systematic and unifying way, stability, convergence and computing results for the different numerical methods for nonlinear elliptic problems. The proofs use linearization, compact perturbation of the coercive principal parts, or monotone operator techniques, and approximation theory. Examples are given for linear to fully nonlinear problems (highest derivatives occur nonlinearly) and for the most important space discretization methods: conforming and nonconforming finite element, discontinuous Galerkin, finite difference, wavelet (and, in a volume to follow, spectral and meshfree) methods. A number of specific long open problems are solved here: numerical methods for fully nonlinear elliptic problems, wavelet and meshfree methods for nonlinear problems, and more general nonlinear boundary conditions. We apply it to all these problems and methods, in particular to eigenvalues, monotone operators, quadrature approximations, and Newton methods. Adaptivity is discussed for finite element and wavelet methods. The book has been written for graduate students and scientists who want to study and to numerically analyze nonlinear elliptic differential equations in Mathematics, Science and Engineering. It can be used as material for graduate courses or advanced seminars.

目次: 

I: ANALYTICAL RESULTS
1. From Linear to Nonlinear Equations, Fundamental Results
2. Analysis for Linear and Nonlinear Elliptic Problems
II: NUMERICAL METHODS
3. A General Discretization Theory
4. Finite Element Methods
5. Nonconforming Finite Element Methods
6. Adaptive Finite Element Methods
7. Discontinuous Galerkin Methods (DCGMs)
8. Finite Difference Methods
9. Variational Methods for Wavelets

著者について: 

Professor Klaus Boehmer took his PhD in Pure and Applied Mathematics in 1969 at the University of Karlsruhe, Germany. He then worked in various universities in Germany and the USA, before becoming full professor at Phillipps University, Marburg, Germany in 1980. He has been a visiting professor at universities in China, the USA and Canada. He retired in 2001.

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