Abstract
Motivated by the idea which has been introduced by M. Haiour and S.Boulaaras (Proc. Indian Acad. Sci. (Math. Sci.) Vol. 121,No. 4, November 2011,pp.481-493), we provide a maximum norm analysis of Euler combined with finite element Schwarz alternating method for a class of parabolic equation on with nolinear source terms two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a stability analysis on Euler scheme which given by our work in (App. Math. Comp., 217, 6443-6450 (2011)), we establish, on each subdomain, an optimal asymptotic behavior between the discrete Schwarz sequence and the asymptotic solution of parabolic differential equations.