A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions
文献类型：期刊论文
| 作者 | Liu, Fang2; Madden, Niall3; Stynes, Martin1; Zhou, Aihui4
|
| 刊名 | IMA JOURNAL OF NUMERICAL ANALYSIS
 |
| 出版日期 | 2009-10-01 |
| 卷号 | 29期号:4页码:986-1007 |
| 关键词 | reaction-diffusion finite element Shishkin mesh two-scale discretization sparse grid |
| ISSN号 | 0272-4979 |
| DOI | 10.1093/imanum/drn048 |
| 英文摘要 | The linear reaction-diffusion problem - epsilon(2)delta u + bu = f is considered on the unit square with homogeneous Dirichlet boundary conditions. Here epsilon is a small positive parameter and the problem is in general singularly perturbed. The numerical solution of this problem is analysed on a Shishkin mesh that has N intervals in each coordinate direction, using the Galerkin finite-element method with bilinear trial functions. The accuracy of this method, measured in the associated energy norm, is shown to be O(N(-2) + epsilon(1/2)N(-1) ln N). It is proved that a two-scale sparse grid method achieves the same order of accuracy while reducing the number of degrees of freedom from O(N(2)) to O(N(3/2)). These results are then generalized to systems of reaction-diffusion equations. |
| 资助项目 | National Natural Science Foundation of China[10701083] ; National Natural Science Foundation of China[10425105] ; National Basic Research Program of China[2005CB321704] ; National University of Ireland, Cork |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000271379100007 |
| 出版者 | OXFORD UNIV PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/7830]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Stynes, Martin |
| 作者单位 | 1.Natl Univ Ireland, Dept Math, Cork, Ireland 2.Cent Univ Finance & Econ, Sch Appl Math, Beijing 100081, Peoples R China 3.Natl Univ Ireland, Dept Math, Galway, Ireland 4.Chinese Acad Sci, Engn Comp Acad Math & Syst Sci, Inst Computat Math & Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Liu, Fang,Madden, Niall,Stynes, Martin,et al. A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2009,29(4):986-1007. |
| APA | Liu, Fang,Madden, Niall,Stynes, Martin,&Zhou, Aihui.(2009).A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions.IMA JOURNAL OF NUMERICAL ANALYSIS,29(4),986-1007. |
| MLA | Liu, Fang,et al."A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions".IMA JOURNAL OF NUMERICAL ANALYSIS 29.4(2009):986-1007. |
入库方式： OAI收割
来源：数学与系统科学研究院
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