Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis (Numerical Mathematics and Scientific Computation) - Hardcover

Bohmer, Klaus

Hardcover

ISBN 10: 0199577048 ISBN 13: 9780199577040

Publisher: Oxford University Press, 2010

Synopsis

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.

About this title

About the Author

Professor Klaus Bohmer 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.

Review

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

Edition details

• Publisher: Oxford University Press
• Publication date: 2010
• ISBN 10: 0199577048
• ISBN 13: 9780199577040
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 776