Overlapping Nonmatching Grids Method: Some Preliminary Studies

In this paper, we report some preliminary studies of a finite difference method on overlapping nonmatching grids for a two-dimensional Poisson problem. The method can be regarded as an extension of the Generalised Additive Schwarz Method (GASM). GASM was originally developed as a preconditioning technique that uses special transmission boundary conditions at the subdomain interfaces. By involving a nonmatching grids interpolation operator in the subdomain boundary conditions, we show that the method can also be used as a discretisation scheme. We focus only on the error issues.