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

A. Harbi, M. Boulbrachene
2011 Journal of Applied Mathematics  
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
more » ... , we establish, on each subdomain, an optimalL∞error estimate between the discrete Schwarz sequence and the exact solution of the PDE.
doi:10.1155/2011/605140 fatcat:dbfbukejvjd6nmgvqbp2y44bwa