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.
Original language | English |
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Article number | 605140 |
Journal | Journal of Applied Mathematics |
Volume | 2011 |
DOIs | |
Publication status | Published - 2011 |
ASJC Scopus subject areas
- Applied Mathematics