國立高雄大學圖資館 |

登入

回首頁

Monotone discretizations for elliptic second order partial differential equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Monotone discretizations for elliptic second order partial differential equationsby Gabriel R. Barrenechea, Volker John, Petr Knobloch.
作者:	Barrenechea, Gabriel R.
其他作者:	John, Volker.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xii, 649 p. :ill. (chiefly color), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Differential equations, EllipticNumerical solutions.
電子資源:	https://doi.org/10.1007/978-3-031-80684-1
ISBN:	9783031806841$q(electronic bk.)

Monotone discretizations for elliptic second order partial differential equations
Barrenechea, Gabriel R.

Monotone discretizations for elliptic second order partial differential equations[electronic resource] /by Gabriel R. Barrenechea, Volker John, Petr Knobloch. - Cham :Springer Nature Switzerland :2025. - xii, 649 p. :ill. (chiefly color), digital ;24 cm. - Springer series in computational mathematics,v. 612198-3712 ;. - Springer series in computational mathematics ;42..

- Introduction. - Convection-Di usion-Reaction Problems and Maximum Principles -- Discrete Maximum Principles -- Partitions of the Domain -- Finite Element Methods -- Finite Element Methods for Diffusion Problems -- Finite Element Methods for Reaction-Diffusion Problems -- Linear Finite Element Methods for Convection-Diffusion-Reaction Problems -- Nonlinear Finite Element Methods for Convection-Diffusion-Reaction Problems: Discretizations Based on Modi ed Variational Forms -- Nonlinear Finite Element Methods for Convection-Diffusion-Reaction Problems: Algebraically Stabilized Methods -- Finite Difference Methods -- Finite Volume Methods -- A Numerical Study for a Problem with Different Regimes -- Outlook.

This book offers a comprehensive presentation of numerical methods for elliptic boundary value problems that satisfy discrete maximum principles (DMPs). The satisfaction of DMPs ensures that numerical solutions possess physically admissible values, which is of utmost importance in numerous applications. A general framework for the proofs of monotonicity and discrete maximum principles is developed for both linear and nonlinear discretizations. Starting with the Poisson problem, the focus is on convection-diffusion-reaction problems with dominant convection, a situation which leads to a numerical problem with multi-scale character. The emphasis of this book is on finite element methods, where classical (usually linear) and modern nonlinear discretizations are presented in a unified way. In addition, popular finite difference and finite volume methods are discussed. Besides DMPs, other important properties of the methods, like convergence, are studied. Proofs are presented step by step, allowing readers to understand the analytic techniques more easily. Numerical examples illustrate the behavior of the methods.

ISBN: 9783031806841$q(electronic bk.)

Standard No.: 10.1007/978-3-031-80684-1doiSubjects--Topical Terms:

229284
Differential equations, Elliptic
--Numerical solutions.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Monotone discretizations for elliptic second order partial differential equations
LDR:02971nmm a2200337 a 4500 001 680465
003 DE-He213
005 20250319115233.0
006 m d
007 cr nn 008maaau
008 251110s2025 sz s 0 eng d
020 $a 9783031806841$q(electronic bk.)
020 $a 9783031806834$q(paper)
024 7 $a 10.1007/978-3-031-80684-1 $2 doi
035 $a 978-3-031-80684-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515.353 $2 23
090 $a QA377 $b .B271 2025
100 1 $a Barrenechea, Gabriel R. $3 761592
245 1 0 $a Monotone discretizations for elliptic second order partial differential equations $h [electronic resource] / $c by Gabriel R. Barrenechea, Volker John, Petr Knobloch.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xii, 649 p. : $b ill. (chiefly color), digital ; $c 24 cm.
490 1 $a Springer series in computational mathematics, $x 2198-3712 ; $v v. 61
505 0 $a - Introduction. - Convection-Di usion-Reaction Problems and Maximum Principles -- Discrete Maximum Principles -- Partitions of the Domain -- Finite Element Methods -- Finite Element Methods for Diffusion Problems -- Finite Element Methods for Reaction-Diffusion Problems -- Linear Finite Element Methods for Convection-Diffusion-Reaction Problems -- Nonlinear Finite Element Methods for Convection-Diffusion-Reaction Problems: Discretizations Based on Modi ed Variational Forms -- Nonlinear Finite Element Methods for Convection-Diffusion-Reaction Problems: Algebraically Stabilized Methods -- Finite Difference Methods -- Finite Volume Methods -- A Numerical Study for a Problem with Different Regimes -- Outlook.
520 $a This book offers a comprehensive presentation of numerical methods for elliptic boundary value problems that satisfy discrete maximum principles (DMPs). The satisfaction of DMPs ensures that numerical solutions possess physically admissible values, which is of utmost importance in numerous applications. A general framework for the proofs of monotonicity and discrete maximum principles is developed for both linear and nonlinear discretizations. Starting with the Poisson problem, the focus is on convection-diffusion-reaction problems with dominant convection, a situation which leads to a numerical problem with multi-scale character. The emphasis of this book is on finite element methods, where classical (usually linear) and modern nonlinear discretizations are presented in a unified way. In addition, popular finite difference and finite volume methods are discussed. Besides DMPs, other important properties of the methods, like convergence, are studied. Proofs are presented step by step, allowing readers to understand the analytic techniques more easily. Numerical examples illustrate the behavior of the methods.
650 0 $a Differential equations, Elliptic $x Numerical solutions. $3 229284
650 0 $a Discretization (Mathematics) $3 821250
650 0 $a Boundary value problems. $3 206979
650 1 4 $a Analysis. $3 273775
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 274020
700 1 $a John, Volker. $3 761607
700 1 $a Knobloch, Petr. $3 732931
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Springer series in computational mathematics ; $v 42. $3 560664
856 4 0 $u https://doi.org/10.1007/978-3-031-80684-1
950 $a Mathematics and Statistics (SpringerNature-11649)