| Issue |
ESAIM: M2AN
Volume 35, Number 2, March/April 2001
|
|
|---|---|---|
| Page(s) | 355 - 387 | |
| DOI | https://doi.org/10.1051/m2an:2001119 | |
| Published online | 15 April 2002 | |
A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
Institut für Angewandte Mathematik, Universität Freiburg,
Hermann-Herderstr. 10, 79104 Freiburg, Germany. (mario@mathematik.uni-freiburg.de)
Received:
20
October
2000
Revised:
29
January
2001
This paper is devoted to the study of a posteriori
error estimates for the scalar nonlinear convection-diffusion-reaction equation
.
The estimates for the error between the exact solution and an upwind finite
volume approximation to the solution are derived in the L1-norm,
independent of the diffusion parameter D.
The resulting a posteriori error estimate is used to define an grid adaptive solution
algorithm for the finite volume scheme. Finally numerical experiments underline
the applicability of the theoretical results.
Mathematics Subject Classification: 65M15 / 35K65 / 76M25
Key words: A posteriori error estimates / convection diffusion reaction equation / finite volume schemes / adaptive methods / unstructured grids.
© EDP Sciences, SMAI, 2001
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