Articles

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

  • Salah BOULAARAS ,
  • Mohammed Said TOUATI ,
  • BRAHIM Smail BOUZENADA ,
  • Abderrahmane ZARAI
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  • 1. Department of Mathematics, College of Sciences and Arts, Al-Ras, Qassim University, Kingdom of Saudi Arabia;
    2. Laboratory of Fundamental and Applied Mathematics of Oran(LMFAO), University of Oran 1, Ahmed Benbella, Oran, Algeria;
    3. Department of Mathematics and Computer Science, Larbi Tebessi University, 12002 Tebessa, Algeria

Received date: 2016-02-06

  Revised date: 2017-08-07

  Online published: 2018-08-25

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.

Cite this article

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 . DOI: 10.1016/S0252-9602(18)30810-5

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