Journal of Applied Mathematics

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

A. Harbi and M. Boulbrachene

Full-text: Open access

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 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

Permanent link to this document
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


Export citation