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 scheme combined with finite element Schwarz alternating method for a class of parabolic equation with nonlinear source terms on 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 the theta 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.
@article{40272,
title = {The maximum norm analysis of a nonmatching grids method for a class of parabolic equation with nonlinear source terms},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {38},
year = {2019},
doi = {10.5269/bspm.v38i4.40272},
language = {EN},
url = {http://dml.mathdoc.fr/item/40272}
}
Boulaaras, Salah; Bahi, Mohammed Cherif; Haiour, Mohamed; Zarai, Abderrahman. The maximum norm analysis of a nonmatching grids method for a class of parabolic equation with nonlinear source terms. Boletim da Sociedade Paranaense de Matemática, Tome 38 (2019) . doi : 10.5269/bspm.v38i4.40272. http://gdmltest.u-ga.fr/item/40272/