| Title:
|
Error estimates for linear finite elements on Bakhvalov-type meshes (English) |
| Author:
|
Roos, Hans-Görg |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
63-72 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For convection-diffusion problems with exponential layers, optimal error estimates for linear finite elements on Shishkin-type meshes are known. We present the first optimal convergence result in an energy norm for a Bakhvalov-type mesh. (English) |
| Keyword:
|
numerical analysis |
| Keyword:
|
convection-diffusion problem |
| Keyword:
|
boundary layer |
| Keyword:
|
uniform convergence |
| MSC:
|
65N12 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| MSC:
|
65N50 |
| idZBL:
|
Zbl 1164.65486 |
| idMR:
|
MR2197323 |
| DOI:
|
10.1007/s10492-006-0005-y |
| . |
| Date available:
|
2009-09-22T18:24:51Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134630 |
| . |
| Reference:
|
[1] A. S. Bakhvalov: On the optimization of methods for solving boundary value problems with boundary layers.Zh. Vychisl. Mat. Mat. Fiz. 9 (1969), 841–859. (Russian) MR 0255066 |
| Reference:
|
[2] T. Linss: Layer-adapted meshes for convection-diffusion problems.Comput. Methods Appl. Mech. Engrg. 192 (2003), 1061–1105. Zbl 1022.76036, MR 1960975, 10.1016/S0045-7825(02)00630-8 |
| Reference:
|
[3] M. Dobrowolski: Finite Elemente.University textbook of Würzburg, 1998. |
| Reference:
|
[4] N. Kopteva, M. Stynes: Approximation of derivatives in a convection-diffusion two-point boundary value problem.Appl. Numer. Math. 39 (2001), 47–60. MR 1855164, 10.1016/S0168-9274(01)00051-4 |
| Reference:
|
[5] H.-G. Roos, T. Linss: Sufficient conditions for uniform convergence on layer-adapted grids.Computing 63 (1999), 27–45. MR 1702159, 10.1007/s006070050049 |
| Reference:
|
[6] H.-G. Roos, M. Stynes, L. Tobiska: Numerical Methods for Singularly Perturbed Differential Equations. Convection-Diffusion and Flow Problems.Springer-Verlag, Berlin, 1996. MR 1477665 |
| Reference:
|
[7] W. W. Shaidurov, B. M. Bagaev, and E. D. Karepova: Numerical Methods for Problems with Boundary Layers II.Nauka, Novosibirsk, 2002. (Russian) MR 2029041 |
| Reference:
|
[8] M. Stynes, E. O’Riordan: A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem.J. Math. Anal. Appl. 214 (1997), 36–54. MR 1645503, 10.1006/jmaa.1997.5581 |
| . |
