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Partial Differential Equations: Modeling, Analysis and Numerical Approximation / by Hervé Le Dret, Brigitte Lucquin.
Springer Nature - Springer Mathematics and Statistics eBooks 2016 English International Available online
View online- Format:
- Book
- Author/Creator:
- Le Dret, H., Author.
- Lucquin, Brigitte, Author.
- Series:
- International Series of Numerical Mathematics, 0373-3149 ; 168
- Language:
- English
- Subjects (All):
- Differential equations, Partial.
- Partial Differential Equations.
- Local Subjects:
- Partial Differential Equations.
- Physical Description:
- 1 online resource (XI, 395 p. 140 illus., 21 illus. in color.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
- Language Note:
- English
- Summary:
- This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems. .
- Contents:
- Foreword
- Mathematical modeling and PDEs
- The finite difference method for elliptic problems
- A review of analysis
- The variational formulation of elliptic PDEs.-Variational approximation methods for elliptic PDEs
- The finite element method in dimension two
- The heat equation
- The finite difference method for the heat equation
- The wave equation
- The finite volume method
- Index
- References.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references and index.
- ISBN:
- 3-319-27067-2
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