Monotone Discretizations for Elliptic Second Order Partial Differential Equations
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 applicati...
Saved in:
| Main Authors: | , , |
|---|---|
| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
|
| Edition: | 1st ed. 2025. |
| Series: | Springer Series in Computational Mathematics,
61 |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/978-3-031-80684-1 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-031-80684-1 | ||
| 003 | DE-He213 | ||
| 005 | 20260706115719.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 250319s2025 sz | s |||| 0|eng d | ||
| 020 | |a 9783031806841 |9 978-3-031-80684-1 | ||
| 024 | 7 | |a 10.1007/978-3-031-80684-1 |2 doi | |
| 050 | 4 | |a QA299.6-433 | |
| 072 | 7 | |a PBK |2 bicssc | |
| 072 | 7 | |a MAT034000 |2 bisacsh | |
| 072 | 7 | |a PBK |2 thema | |
| 082 | 0 | 4 | |a 515 |2 23 |
| 100 | 1 | |a Barrenechea, Gabriel R. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 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. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a XII, 649 p. 160 illus., 124 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Springer Series in Computational Mathematics, |x 2198-3712 ; |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 Mathematical analysis. | |
| 650 | 0 | |a Mathematics |x Data processing. | |
| 650 | 1 | 4 | |a Analysis. |
| 650 | 2 | 4 | |a Computational Mathematics and Numerical Analysis. |
| 700 | 1 | |a John, Volker. |e author. |0 (orcid)0000-0002-2711-4409 |1 https://orcid.org/0000-0002-2711-4409 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Knobloch, Petr. |e author. |0 (orcid)0000-0003-2709-5882 |1 https://orcid.org/0000-0003-2709-5882 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031806834 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031806858 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031806865 |
| 830 | 0 | |a Springer Series in Computational Mathematics, |x 2198-3712 ; |v 61 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-80684-1 |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 912 | |a ZDB-2-251 | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||
| 950 | |a Focus Bundle Mathematics and Statistics (SpringerNature-85421) | ||