An Adaptive Multi-level method for Convection Diffusion Problems
UMR CNRS 5585, Département Mathématique-Informatique,
École Centrale de Lyon, BP 163, 69131 Écully Cedex, France.
2 UMR CNRS 5640, Département Génie Mathématique, INSA, Complexe de Rangueil, 31077 Toulouse Cedex 4, France.
Revised: 13 December 1999
In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an a posteriori error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem.
Mathematics Subject Classification: 65M15 / 65M25 / 65M70 / 76R99
Key words: Multi-level methods / convection-diffusion equations / characteristics method / a posteriori error estimates / adaptive algorithms.
© EDP Sciences, SMAI, 2000