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Variational boundary integral equations for the Stokes system§

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Abstract:

In this article, we analyze the variational formulations of the direct boundary integral equations for the Dirichlet, the Neumann, and the mixed boundary value problems of the Stokes system in on Lipschitz boundaries. Although the Stokes system does not belong to the class of formally positive elliptic second-order systems in the sense of Vishik and Schechter, its close relation to the Lamé system of elastostatics, together with Green's identities imply also here Gårding inequalities and coerciveness properties of the hydrodynamic boundary potentials. As a consequence, the well-developed fast multipole boundary element methods of 3D elasticity can be applied for solving the Stokes system as well. §Dedicated to Prof. Dr. Dr.h.c. Ioan A. Rus on the occasion of his 70th birthday.

Keywords: Boundary integral equations; Coerciveness and mapping properties of Stokes boundary layer potentials in Sobolev–Slobodetski spaces on Lipschitz boundaries; Fast multipole boundary element methods

Document Type: Research Article

DOI: https://doi.org/10.1080/00036810600963961

Affiliations: 1: Faculty of Mathematics and Computer Science, BabeÅŸ-Bolyai University, 1 M. Kogălniceanu Str, 400084 Cluj-Napoca, Romania 2: Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Publication date: 2006-11-01

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