| Title:
|
Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D (English) |
| Author:
|
Roos, Hans-Görg |
| Author:
|
Schopf, Martin |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
97-108 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions. (English) |
| Keyword:
|
finite element method |
| Keyword:
|
singular perturbation |
| Keyword:
|
convection-diffusion problem |
| Keyword:
|
Bakhvalov-type meshes |
| Keyword:
|
layer-adapted meshes |
| Keyword:
|
optimal error estimates |
| Keyword:
|
exponential boundary layers |
| MSC:
|
35B25 |
| MSC:
|
35J25 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| MSC:
|
65N50 |
| idZBL:
|
Zbl 1249.65248 |
| idMR:
|
MR2899726 |
| DOI:
|
10.1007/s10492-012-0007-x |
| . |
| Date available:
|
2012-03-05T06:59:26Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142030 |
| . |
| Reference:
|
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| Reference:
|
[2] Franz, S.: Singularly perturbed problems with characteristic layers.PHD TU Dresden (2008). Zbl 1302.35002 |
| Reference:
|
[3] Linß, T.: Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem.IMA J. Numer. Anal. 20 (2000), 621-632. Zbl 0966.65083, MR 1795300, 10.1093/imanum/20.4.621 |
| Reference:
|
[4] Linß, T.: Uniform superconvergence of a Galerkin finite element method on Shishkin-type meshes.Numer. Methods Partial Differential Equations 16 (2000), 426-440. MR 1778398, 10.1002/1098-2426(200009)16:5<426::AID-NUM2>3.0.CO;2-R |
| Reference:
|
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| Reference:
|
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| Reference:
|
[7] O'Riordan, E., Shiskin, G.: A technique to prove parameter-uniform convergence for a singularly perturbed convection-diffusion equation.J. Comput. Appl. Math. 206 (2007), 136-145. MR 2333841, 10.1016/j.cam.2006.06.002 |
| Reference:
|
[8] Roos, H.-G., Lin{ß}, T.: Sufficient conditions for uniform convergence on layer-adapted grids.Computing 63 (1999), 27-45. Zbl 0931.65085, MR 1702159, 10.1007/s006070050049 |
| Reference:
|
[9] Roos, H.-G.: Error estimates for linear finite elements on Bakhvalov-type meshes.Appl. Math. 51 (2006), 63-72. Zbl 1164.65486, MR 2197323, 10.1007/s10492-006-0005-y |
| Reference:
|
[10] Roos, H.-G., Stynes, M., Tobiska, L.: Robust Numerical Methods for Singularly Perturbed Differential Equations.Springer Berlin (2008). Zbl 1155.65087, MR 2454024 |
| Reference:
|
[11] Stynes, M., O'Riordan, E.: A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem.J. Math. Anal. Appl. 214 (1997), 36-54. Zbl 0917.65088, MR 1645503, 10.1006/jmaa.1997.5581 |
| Reference:
|
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| . |
