A Robin-type non-overlapping domain decomposition procedure for second order elliptic problems

Abstract

This article deals with the analysis of an iterative non-overlapping domain decomposition (DD) method for elliptic problems, using Robin-type boundary condition on the inter-subdomain boundaries, which can be solved in parallel with local communications. The proposed iterative method allows us to relax the continuity condition for Lagrange multipliers on the inter-subdomain boundaries. In order to derive the corresponding discrete problem, we apply a non-conforming Galerkin method using lowest order Crouzeix–Raviart elements. The convergence of the iterative scheme is obtained by proving that the spectral radius of the matrix associated with the fixed point iterations is less than 1. Parallel computations have been carried out and the numerical experiments confirm the theoretical results established in this paper.