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

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doi:10.1016/S0252-9602(18)30810-5

Abstract:

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.

Key words: a posteriori error estimates, GODDM, advection-diffusion, Galerkin method, Benssoussan-Lions'algorithm

Salah BOULAARAS, Mohammed Said TOUATI, BRAHIM Smail BOUZENADA, Abderrahmane ZARAI. AN ASYMPTOTIC BEHAVIOR AND A POSTERIORI ERROR ESTIMATES FOR THE GENERALIZED SCHWARTZ METHOD OF ADVECTION-DIFFUSION EQUATION[J].Acta mathematica scientia,Series B, 2018, 38(4): 1227-1244.

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