Finite Volume Methods for Domain Decomposition on Nonmatching Grids with Arbitrary Interface Conditions

Abstract

We are interested in a robust and accurate domain decomposition method with arbitrary interface conditions on nonmatching multiblock grids using a finite volume discretization. To take into account the nonmatching grids at the interface, we introduce transmission operators, Dirichlet--Neumann interface conditions, and arbitrary equivalent interface conditions (for example, Robin interface conditions). Under a compatibility assumption on the transmission operators, we prove the equivalence between the different types of interface conditions and the well posedness of the local and global problems. Then two error estimates are proven in terms of the discrete H1-norm: the first in O(h)1/2 with transmission operators based on piecewise constant functions and the second in O(h) (as in the matching case) with transmission operators using a piecewise linear rebuilding. In conclusion, numerical results are presented in confirmation of the theory.