AN ASYMPTOTIC BEHAVIOR AND A POSTERIORI ERROR ESTIMATES FOR THE GENERALIZED SCHWARTZ METHOD OF ADVECTION-DIFFUSION EQUATION

摘要

In this paper,a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are proved by using the Euler time scheme combined with Galerkin spatial method.Furthermore,an asymptotic behavior in Sobolev norm is deduced using Benssoussan-Lions' algorithm.Finally,the results of some numerical experiments are presented to support the theory.