國立高雄大學圖資館 |

Language: English

Back

Numerical methods for elliptic and p...

Angermann, Lutz.

Numerical methods for elliptic and parabolic partial differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical methods for elliptic and parabolic partial differential equationsby Peter Knabner, Lutz Angermann ; with contributions by Andreas Rupp.
Author:	Knabner, Peter.
other author:	Angermann, Lutz.
Published:	Cham :Springer International Publishing :2021.
Description:	xix, 802 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations, PartialNumerical solutions.
Online resource:	https://doi.org/10.1007/978-3-030-79385-2
ISBN:	9783030793852$q(electronic bk.)

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 ;40..

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$q(electronic bk.)

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

185034
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
LDR:03160nmm 22003495a 4500 001 614058
003 DE-He213
005 20211119095220.0
006 m d
007 cr nn 008maaau
008 220627s2021 sz s 0 eng d
020 $a 9783030793852$q(electronic bk.)
020 $a 9783030793845$q(paper)
024 7 $a 10.1007/978-3-030-79385-2 $2 doi
035 $a 978-3-030-79385-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377 $b .K53 2021
072 7 $a PBKS $2 bicssc
072 7 $a MAT021000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 515.353 $2 23
090 $a QA377 $b .K67 2021
100 1 $a Knabner, Peter. $3 345321
245 1 0 $a Numerical methods for elliptic and parabolic partial differential equations $h [electronic resource] / $c by Peter Knabner, Lutz Angermann ; with contributions by Andreas Rupp.
250 $a Second extended edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xix, 802 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Texts in applied mathematics, $x 2196-9949 ; $v v. 44
505 0 $a 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.
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.
650 0 $a Differential equations, Partial $x Numerical solutions. $3 185034
650 1 4 $a Numerical Analysis. $3 275681
650 2 4 $a Analysis. $3 273775
650 2 4 $a Applications of Mathematics. $3 273744
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 274020
650 2 4 $a Numerical and Computational Physics, Simulation. $3 758154
650 2 4 $a Mathematical and Computational Engineering. $3 775095
700 1 $a Angermann, Lutz. $3 345320
700 1 $a Rupp, Andreas. $3 912206
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Texts in applied mathematics ; $v 40. $3 558788
856 4 0 $u https://doi.org/10.1007/978-3-030-79385-2
950 $a Mathematics and Statistics (SpringerNature-11649)