Domain decomposition for a finite volume method on non-matching grids

Abstract

We are interested in a robust and accurate domain decomposition method with Robin interface conditions on non-matching grids using a finite volume discretization. We introduce transmission operators on the non-matching grids and define new interface conditions of Robin type. Under a compatibility assumption, we show the equivalence between Robin interface conditions and Dirichlet–Neumann interface conditions and the well-posedness of the global and local problems. Two error estimates are given in terms of the discrete H 1-norm: one in O( h 1/2) with operators based on piecewise constant functions and the other in O( h) (as in the conforming case) with operators using a linear rebuilding. Numerical results are given. To cite this article: L. Saas et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).