Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis by Klaus Boehmer

Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

byKlaus Boehmer

Hardcover | October 30, 2010

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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 thedifferent 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 occurnonlinearly) 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: numericalmethods 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.

About The Author

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 Ca...

Details & Specs

Title:Numerical Methods for Nonlinear Elliptic Differential Equations: A SynopsisFormat:HardcoverDimensions:720 pages, 9.69 × 6.73 × 0.03 inPublished:October 30, 2010Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199577048

ISBN - 13:9780199577040

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Table of Contents

Part I: Analytical Results1. From Linear to Nonlinear Equations, Fundamental Results2. Analysis for Linear and Nonlinear Elliptic ProblemsPart II: Numerical Methods3. A General Discretization Theory4. O. Davydov: Finite Element Methods5. Nonconforming Finite Element Methods6. W. Doerfler: Adaptive Finite Element Methods7. V. Dolejsi: Discontinuous Galerkin Methods (DCGMs)8. Finite Difference Methods9. S. Dahlke and T. Raasch: Variational Methods for Wavelets

Editorial Reviews

Review from previous edition: "This book could become the classic reference on the subject ... an important reference as a source for seminars and advanced courses in numerical analysis and nonlinear science." --Eugene Allgower, Colorado State University