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Error of an eFDDM: What Do Matched Asymptotic Expansions Teach Us?

  • Jérôme MichaudEmail author
  • Pierre-Henri Cocquet
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)

Abstract

In this paper, we analyze the approximation error of an explicit Fuzzy Domain Decomposition Method (eFDDM) (Gander and Michaud, Fuzzy domain decomposition: a new perspective on heterogeneous DD methods, in Domain Decomposition Methods in Science and Engineering XXI, ed. by J. Erhel, M.J. Gander, L. Halpern, G. Pichot, T. Sassi, O.B. Widlund. Lecture Notes in Computational Science and Engineering. Springer, Berlin, 2013) using matched asymptotic expansions (Cousteix and Mauss, Asymptotic Analysis and Boundary Layers, Springer, Berlin, 2007). We show that the global convergence of the method for an advection dominated diffusion problem is of order \(\mathcal{O}(\nu )\) and have numerical evidence that the method is of order \(\mathcal{O}(\nu ^{3/2})\) in the boundary layer. Our results generalize the results of Gander and Martin (An asymptotic approach to compare coupling mechanisms for different partial differential equations, in Domain Decomposition Methods in Science and Engineering XX, ed. by R. Bank, M. Holst, O.B. Widlund, J. Xu. Lecture Notes in Computational Science and Engineering, Springer, Berlin, 2012) to this new method and show that the eFDDM is a viable alternative to other coupling methods.

Keywords

Boundary Layer Approximation Error Membership Function Domain Decomposition Coupling Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Université de Genève2-4 rue du LièvreGenève 4Switzerland

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