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Numerical treatment of partial differential equations. Revised translation of the 3rd German edition of ‘Numerische Behandlung partieller Differentialgleichungen’ by Martin Stynes. (English) Zbl 1180.65147
Universitext. Berlin: Springer (ISBN 978-3-540-71582-5/pbk). xii, 591 p. (2007).
Publisher’s description: This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques.
Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research with detailed introductions to such recent topics as a posteriori error estimation, discontinuous Galerkin methods or optimal control with partial differential equations. In addition, the authors give basic facts on how to solve generated discrete problems. Chapters on singularly perturbed problems, variational inequalities and optimal control reflect the research interests of the authors.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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