Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/8056
Title: Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM
Authors: Gatica, GN
Maischak, M
Stephan, EP
Keywords: Raviart-Thomas space;Boundary integral operator;Lagrange multiplier
Issue Date: 2011
Publisher: Cambridge University Press
Citation: ESAIM: Mathematical Modelling and Numerical Analysis, 45(4), 779 - 802, 2011
Abstract: This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in Rn (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc := Rn\ ̄Ω. The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping (NtD) given in terms of boundary integral operators. The resulting variational formulation becomes a variational inequality with a linear operator. Then we treat the corresponding numerical scheme and discuss an approximation of the NtD mapping with an appropriate discretization of the inverse Poincar´e-Steklov operator. In particular, assuming some abstract approximation properties and a discrete inf-sup condition, we show unique solvability of the discrete scheme and obtain the corresponding a-priori error estimate. Next, we prove that these assumptions are satisfied with Raviart- Thomas elements and piecewise constants in Ω, and continuous piecewise linear functions on Γ. We suggest a solver based on a modified Uzawa algorithm and show convergence. Finally we present some numerical results illustrating our theory.
Description: © EDP Sciences, SMAI 2011
URI: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8119330
http://bura.brunel.ac.uk/handle/2438/8056
DOI: http://dx.doi.org/10.1051/m2an/2010102
ISSN: 0764-583X
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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