| Issue |
ESAIM: M2AN
Volume 49, Number 5, September-October 2015
|
|
|---|---|---|
| Page(s) | 1525 - 1547 | |
| DOI | https://doi.org/10.1051/m2an/2015027 | |
| Published online | 15 September 2015 | |
Layer structure and the galerkin finite element method for a system of weakly coupled singularly perturbed convection-diffusion equations with multiple scales
University of Technology Dresden, 01062
Dresden,
Germany
Hans-Goerg.Roos@tu-dresden.de; Martin.Schopf@outlook.de
Received:
30
September
2014
Revised:
11
March
2015
We consider a system of weakly coupled singularly perturbed convection-diffusion equations with multiple scales. Based on sharp estimates for first order derivatives, Linß [T. Linß, Computing 79 (2007) 23–32.] analyzed the upwind finite-difference method on a Shishkin mesh. We derive such sharp bounds for second order derivatives which show that the coupling generates additional weak layers. Finally, we prove the first robust convergence result for the Galerkin finite element method for this class of problems on modified Shishkin meshes introducing a mesh grading to cope with the weak layers. Numerical experiments support our theory.
Mathematics Subject Classification: 34E15 / 34A30 / 65L10 / 65L11 / 65L60 / 65L70
Key words: Convection-diffusion / graded mesh / Shishkin mesh / singular perturbation / system of differential equations / uniform convergence
© EDP Sciences, SMAI, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.