A cell functional minimization scheme for domain decomposition method on non-orthogonal and non-matching meshes

Abstract

We are interested in a robust and accurate domain decomposition algorithm with interface conditions of Robin type on non-matching multiblock grids using a cell functional minimization scheme, which has a good performance on non-orthogonal meshes. In order to treat the non-matching grids at the interface, we introduce the $$L^2$$ L 2 projection operator to ensure weak continuity of the primary unknown and of the normal flux across the non-matching interface. Furthermore, we prove the wellposedness of local and global problems and obtain as well an error estimate of first order in a discrete $$H^{1}$$ H 1 -norm only using the $$L^{2}$$ L 2 projection operator on the non-matching interface, as done in the matching case. Numerical results are presented in confirmation of the theoretical results.