Layer-adapted meshes for reaction-convection-diffusion problems / by Torsten LinB
- 作者： LinB, Torsten.
- 其他作者：
- 其他題名：
- Springer eBooks
- 出版： Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg 2010
- 叢書名： Lecture notes in mathematics ,1985
- 主題： Reaction-diffusion equations. , Finite volume method. , Mathematics. , Numerical analysis. , Ordinary Differential Equations. , Partial Differential Equations.
- ISBN： 9783642051340 (electronic bk.) 、 9783642051333 (paper)
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電子書
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讀者標籤：
- 系統號： 005173124 | 機讀編目格式
館藏資訊
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.