A posteriori error analysis for two non-overlapping domain decomposition techniques
Applied Numerical Mathematics(2009)
Abstract
This paper is devoted to the construction of fast solvers for penalty domain decomposition techniques, based upon a posteriori error analysis. We introduce a penalty non-overlapping domain decomposition method (ddm) motivated by the a posteriori error analysis of the method proposed by Chacon and Chacon in [T. Chacon Rebollo, E. Chacon Vera, A non-overlapping domain decomposition method for the Stokes equations via a penalty term on the interface, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1-16]. In the new method a H"0"0^1^/^2(@C) penalty term replaces the L^2(@C) one in the original method. The number of iterations needed by the new ddm to yield a solution with an error of the same order as the discretization error is remarkably reduced. We develop an a posteriori error analysis that we use to determine an optimal value of the penalty parameter for a given grid, and also to jointly determine an optimal grid and a penalty parameter to reduce the error below a targeted value. Several numerical tests for model problems exhibit the good performances of our approach and provide to a numerical comparison of the two penalty methods.
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Key words
non-overlapping domain decomposition technique,domain decomposition method,discretization error,penalty term,original method,non-overlapping domain decomposition method,penalty method,penalty domain decomposition technique,new method,posteriori error analysis,penalty parameter,stokes equation,finite element,domain decomposition
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