| Title:
|
The combination technique for a two-dimensional convection-diffusion problem with exponential layers (English) |
| Author:
|
Franz, Sebastian |
| Author:
|
Liu, Fang |
| Author:
|
Roos, Hans-Görg |
| Author:
|
Stynes, Martin |
| Author:
|
Zhou, Aihui |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
54 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
203-223 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing $N$ for the maximum number of mesh intervals in each coordinate direction, our ``combination'' method simply adds or subtracts solutions that have been computed by the Galerkin FEM on $N \times \sqrt N$, $\sqrt N \times N$ and $\sqrt N \times \sqrt N$ meshes. It is shown that the combination FEM yields (up to a factor $\ln N$) the same order of accuracy in the associated energy norm as the Galerkin FEM on an $N\times N$ mesh, but it requires only $\Cal O(N^{3/2})$ degrees of freedom compared with the $\Cal O(N^2)$ used by the Galerkin FEM. An analogous result is also proved for the streamline diffusion finite element method. (English) |
| Keyword:
|
convection-diffusion |
| Keyword:
|
finite element |
| Keyword:
|
Shishkin mesh |
| Keyword:
|
two-scale discretization |
| Keyword:
|
exponential layers |
| Keyword:
|
Galerkin FEM |
| MSC:
|
65F10 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| MSC:
|
65N55 |
| MSC:
|
65Y10 |
| idZBL:
|
Zbl 1212.65443 |
| idMR:
|
MR2530539 |
| DOI:
|
10.1007/s10492-009-0013-9 |
| . |
| Date available:
|
2010-07-20T12:58:20Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140360 |
| . |
| Reference:
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