東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Numerical methods for nonlinear part...

Bartels, Soren.

Linked to FindBook

Google Book

Amazon

博客來

Numerical methods for nonlinear partial differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical methods for nonlinear partial differential equations/ by Soren Bartels.
Author:	Bartels, Soren.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	x, 393 p. :ill., digital ;24 cm.
[NT 15003449]:	1. Introduction -- Part I: Analytical and Numerical Foundations -- 2. Analytical Background -- 3. FEM for Linear Problems -- 4. Concepts for Discretized Problems -- Part II: Approximation of Classical Formulations -- 5. The Obstacle Problem -- 6. The Allen-Cahn Equation -- 7. Harmonic Maps -- 8. Bending Problems -- Part III: Methods for Extended Formulations -- 9. Nonconvexity and Microstructure -- 10. Free Discontinuities -- 11. Elastoplasticity -- Auxiliary Routines -- Frequently Used Notation -- Index.
Contained By:	Springer eBooks
Subject:	Differential equations, Partial - Numerical solutions. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-13797-1
ISBN:	9783319137971 (electronic bk.)

Numerical methods for nonlinear partial differential equations
Bartels, Soren.

Numerical methods for nonlinear partial differential equations[electronic resource] /by Soren Bartels. - Cham :Springer International Publishing :2015. - x, 393 p. :ill., digital ;24 cm. - Springer series in computational mathematics,v.470179-3632 ;. - Springer series in computational mathematics ;42..

1. Introduction -- Part I: Analytical and Numerical Foundations -- 2. Analytical Background -- 3. FEM for Linear Problems -- 4. Concepts for Discretized Problems -- Part II: Approximation of Classical Formulations -- 5. The Obstacle Problem -- 6. The Allen-Cahn Equation -- 7. Harmonic Maps -- 8. Bending Problems -- Part III: Methods for Extended Formulations -- 9. Nonconvexity and Microstructure -- 10. Free Discontinuities -- 11. Elastoplasticity -- Auxiliary Routines -- Frequently Used Notation -- Index.

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

ISBN: 9783319137971 (electronic bk.)

Standard No.: 10.1007/978-3-319-13797-1doiSubjects--Topical Terms:

540504
Differential equations, Partial
--Numerical solutions.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Numerical methods for nonlinear partial differential equations
LDR:02414nmm a2200337 a 4500 001 1995044
003 DE-He213
005 20150903133057.0
006 m d
007 cr nn 008maaau
008 151019s2015 gw s 0 eng d
020 $a 9783319137971 (electronic bk.)
020 $a 9783319137964 (paper)
024 7 $a 10.1007/978-3-319-13797-1 $2 doi
035 $a 978-3-319-13797-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377
072 7 $a PBKS $2 bicssc
072 7 $a MAT021000 $2 bisacsh
072 7 $a MAT006000 $2 bisacsh
082 0 4 $a 515.353 $2 23
090 $a QA377 $b .B283 2015
100 1 $a Bartels, Soren. $3 2134220
245 1 0 $a Numerical methods for nonlinear partial differential equations $h [electronic resource] / $c by Soren Bartels.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a x, 393 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer series in computational mathematics, $x 0179-3632 ; $v v.47
505 0 $a 1. Introduction -- Part I: Analytical and Numerical Foundations -- 2. Analytical Background -- 3. FEM for Linear Problems -- 4. Concepts for Discretized Problems -- Part II: Approximation of Classical Formulations -- 5. The Obstacle Problem -- 6. The Allen-Cahn Equation -- 7. Harmonic Maps -- 8. Bending Problems -- Part III: Methods for Extended Formulations -- 9. Nonconvexity and Microstructure -- 10. Free Discontinuities -- 11. Elastoplasticity -- Auxiliary Routines -- Frequently Used Notation -- Index.
520 $a The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
650 0 $a Differential equations, Partial $x Numerical solutions. $3 540504
650 0 $a Differential equations, Nonlinear. $3 604084
650 0 $a Numerical analysis. $3 517751
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Numerical Analysis. $3 892626
650 2 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Algorithms. $3 536374
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 898674
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Springer series in computational mathematics ; $v 42. $3 1568666
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-13797-1
950 $a Mathematics and Statistics (Springer-11649)