## Journal of Applied Mathematics

### Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES

#### Abstract

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE 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 Lipschitz asssumption on the nonlinearity, we establish, on each subdomain, an optimal ${L}^{\infty }$ error estimate between the discrete Schwarz sequence and the exact solution of the PDE.

#### Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 605140, 18 pages.

Dates
First available in Project Euclid: 15 March 2012

https://projecteuclid.org/euclid.jam/1331818661

Digital Object Identifier
doi:10.1155/2011/605140

Mathematical Reviews number (MathSciNet)
MR2846447

Zentralblatt MATH identifier
1235.65134

#### Citation

Harbi, A.; Boulbrachene, M. Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES. J. Appl. Math. 2011 (2011), Article ID 605140, 18 pages. doi:10.1155/2011/605140. https://projecteuclid.org/euclid.jam/1331818661