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

Created from the Publication Database of the Vienna University of Technology.