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Title
Numerical methods for elliptic and parabolic partial differential equations / Peter Knabner, Lutz Angermann ; with contributions by Andreas Rupp.
Edition
Second extended edition.
ISBN
9783030793852 (electronic bk.)
3030793850 (electronic bk.)
9783030793845 (print)
Published
Cham, Switzerland : Springer, 2021.
Language
English
Description
1 online resource (xix, 802 pages) : illustrations (some color)
Item Number
10.1007/978-3-030-79385-2 doi
Call Number
QA377
Dewey Decimal Classification
515/.353
Summary
This graduate-level text provides an application oriented introduction to the numerical methods for elliptic and parabolic 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. For students with mathematics major it is an excellent introduction to the theory and methods, guiding them in the selection of methods and helping them to understand and pursue finite element programming. For engineering and physics students it provides a general framework for the formulation and analysis of methods. This second edition sees additional chapters on mixed discretization and on generalizing and unifying known approaches; broader applications on systems of diffusion, convection and reaction; enhanced chapters on node-centered finite volume methods and methods of convection-dominated problems, specifically treating the now-popular cell-centered finite volume method; and the consideration of realistic formulations beyond the Poisson's equation for all models and methods.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed November 29, 2021).
Series
Texts in applied mathematics ; 44.
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.
