Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
SIAM Journal on Numerical Analysis
Timely Communicaton: An Analysis for a Nonoverlapping Domain Decomposition Iterative Procedure
SIAM Journal on Scientific Computing
Optimized Schwarz Methods without Overlap for the Helmholtz Equation
SIAM Journal on Scientific Computing
Poincaré-Friedrichs Inequalities for Piecewise H1 Functions
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Optimized Schwarz Methods with Robin Transmission Conditions for Parabolic Problems
SIAM Journal on Scientific Computing
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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.