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J. Melenk, D. Praetorius, B. Wohlmuth:
"Simultaneous quasi-optimal convergence in FEM-BEM coupling";
in: "ASC Report 13/2014", issued by: Institute of Applied Mathematics and Numerical Analysis; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 21.

We consider the symmetric FEM-BEM coupling that connects two linear
elliptic second order partial differential equations posed in a
bounded domain Ω and its complement, where the exterior problem is
restated by an integral equation on the coupling boundary Gamma. We
assume that the corresponding transmission problem admits a shift
theorem by more than 1/2. We analyze the discretization by piecewise
polynomials of degree k for the domain variable and piecewise
polynomials of degree k-1 for the flux variable on the coupling
boundary. Given sufficient regularity we show that (up to logarithmic
factors) the optimal convergence order k+1/2 in the H^{−1/2}-norm
is obtained for the flux variable, while classical arguments by
Cea-type quasi-optimality and standard approximation results provide
only convergence order k for the overall error in the natural
product norm.

FEM-BEM coupling, a priori convergence analysis, transmission problem

http://www.asc.tuwien.ac.at/preprint/2014/asc13x2014.pdf