Numerical methods for elliptic and parabolic partial differential equations
著者
書誌事項
Numerical methods for elliptic and parabolic partial differential equations
（Texts in applied mathematics, 44）
Springer, c2021
2nd extended edition
- [: hbk.]
- タイトル別名
-
Numerik partieller Differentialgleichungen
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
目次
For Example: Modelling Processes in Porous Media with Differential Equations.- For the Beginning: The Finite Difference Method for the Poisson Equation.- The Finite Element Method for the Poisson Equation.- The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order.- Grid Generation and A Posteriori Error Estimation.- Iterative Methods for Systems of Linear Equations.- Beyond Coercivity, Consistency and Conformity.- Mixed and Nonconforming Discretization Methods.- The Finite Volume Method.- Discretization Methods for Parabolic Initial Boundary Value Problems.- Discretization Methods for Convection-Dominated Problems.- An Outlook to Nonlinear Partial Differential Equations.- Appendices.
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