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Numerical methods for elliptic and p...

Knabner, Peter.

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Numerical methods for elliptic and parabolic partial differential equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Numerical methods for elliptic and parabolic partial differential equations/ by Peter Knabner, Lutz Angermann ; with contributions by Andreas Rupp.
作者:	Knabner, Peter.
其他作者:	Angermann, Lutz.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	xix, 802 p. :ill. (some col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Differential equations, Partial - Numerical solutions. -
電子資源:	https://doi.org/10.1007/978-3-030-79385-2
ISBN:	9783030793852

Numerical methods for elliptic and parabolic partial differential equations
Knabner, Peter.

Numerical methods for elliptic and parabolic partial differential equations[electronic resource] /by Peter Knabner, Lutz Angermann ; with contributions by Andreas Rupp. - Second extended edition. - Cham :Springer International Publishing :2021. - xix, 802 p. :ill. (some col.), digital ;24 cm. - Texts in applied mathematics,v. 442196-9949 ;. - Texts in applied mathematics ;v. 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.

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.

ISBN: 9783030793852

Standard No.: 10.1007/978-3-030-79385-2doiSubjects--Topical Terms:

540504
Differential equations, Partial
--Numerical solutions.

LC Class. No.: QA377 / .K53 2021

Dewey Class. No.: 515.353

Numerical methods for elliptic and parabolic partial differential equations
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520 $a 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.
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