A Robust Adaptive Grid Method for a System of Two Singularly Perturbed Convection-Diffusion Equations with Weak Coupling
- 294 Downloads
A system of singularly perturbed convection-diffusion equations with weak coupling is considered. The system is first discretized by an upwind finite difference scheme for which an a posteriori error estimate in the maximum norm is constructed. Then the a posteriori error bound is used to design an adaptive gird algorithm. Finally, a first-order rate of convergence, independent of the perturbation parameters, is established by using the theory of the discrete Green’s function. Numerical results are presented to illustrate support our theoretical results.
KeywordsConvection-diffusion Adaptive method A posteriori error estimate Weak coupling
Mathematics Subject Classification (1991)65L10 65L12 65L50
- 20.Liu, L.-B., Chen, Y.: A robust grid method for a strongly coupled system of two singularly perturbed convection-diffusion problems. submittedGoogle Scholar