Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems
Singular perturbation problems are discussed in this text, with a focus on the construction and analysis of numerical methods on layer-adapted meshes. Classifications and surveys of layer-adapted meshes are included, for a variety of boundary-value problems.
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| Published in | Lecture notes in mathematics Vol. 1985 |
|---|---|
| Main Author | |
| Format | eBook Book |
| Language | English |
| Published |
Berlin, Heidelberg
Springer Nature
2009
Springer Springer Berlin / Heidelberg Springer Berlin Heidelberg |
| Edition | 1 |
| Series | Lecture Notes in Mathematics |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783642051340 3642051340 9783642051333 3642051332 |
| ISSN | 0075-8434 1617-9692 |
| DOI | 10.1007/978-3-642-05134-0 |
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| Abstract | Singular perturbation problems are discussed in this text, with a focus on the construction and analysis of numerical methods on layer-adapted meshes. Classifications and surveys of layer-adapted meshes are included, for a variety of boundary-value problems. |
|---|---|
| AbstractList | This is a book on numerical methods for singular perturbation problems - in part- ular, stationary reaction-convection-diffusion problems exhibiting layer behaviour. More precisely, it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. Numerical methods for singularly perturbed differential equations have been studied since the early 1970s and the research frontier has been constantly - panding since. A comprehensive exposition of the state of the art in the analysis of numerical methods for singular perturbation problems is [141] which was p- lished in 2008. As that monograph covers a big variety of numerical methods, it only contains a rather short introduction to layer-adapted meshes, while the present book is exclusively dedicated to that subject. An early important contribution towards the optimisation of numerical methods by means of special meshes was made by N.S. Bakhvalov [18] in 1969. His paper spawned a lively discussion in the literature with a number of further meshes - ing proposed and applied to various singular perturbation problems. However, in the mid 1980s, this development stalled, but was enlivened again by G.I. Shishkin's proposal of piecewise-equidistant meshes in the early 1990s [121,150]. Because of their very simple structure, they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on c- peting meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue. Singular perturbation problems are discussed in this text, with a focus on the construction and analysis of numerical methods on layer-adapted meshes. Classifications and surveys of layer-adapted meshes are included, for a variety of boundary-value problems. |
| Author | Linß, Torsten |
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| Notes | Includes bibliographical reference (p. 311-318) and index |
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| Snippet | Singular perturbation problems are discussed in this text, with a focus on the construction and analysis of numerical methods on layer-adapted meshes.... This is a book on numerical methods for singular perturbation problems - in part- ular, stationary reaction-convection-diffusion problems exhibiting layer... |
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| SubjectTerms | Exact sciences and technology Finite volume method General mathematics General, history and biography Mathematics Mathematics and Statistics Numerical Analysis Ordinary Differential Equations Partial Differential Equations Reaction-diffusion equations Reaction-diffusion equations -- Numerical solutions Sciences and techniques of general use Singular perturbations (Mathematics) |
| TableOfContents | Intro -- Preface -- Contents -- Notation -- Introduction -- Layer-Adapted Meshes -- The Analytical Behaviour of Solutions -- Finite Difference Schemes for Convection- Diffusion Problems -- Finite Element and Finite Volume Methods -- Discretisations of Reaction-Convection-Diffusion Problems -- The Analytical Behaviour of Solutions -- Reaction-Diffusion Problems -- Convection-Diffusion Problems -- Conclusions and Outlook -- References -- Index -- Lecture Notes in Mathematics |
| Title | Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems |
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