T. Führer, D. Praetorius:
"A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems";
Computers and Mathematics with Applications, 75 (2018), 8; S. 2678 - 2697.

Kurzfassung englisch:
We propose a fully discrete Uzawa-type iteration for the Johnson-Nédélec
formulation of a Laplace-type transmission problem with possible (strongly monotone)
nonlinearity in the interior domain. In each step, we sequentially solve one BEM for the
weakly-singular integral equation associated with the Laplace-operator and one FEM
for the linear Yukawa equation. In particular, the nonlinearity is only evaluated to
build the right-hand side of the Yukawa equation. The algorithm includes the inexact
solution of the BEM/FEM part by a preconditioned CG method. We prove that the
proposed method leads to linear convergence with respect to the number of Uzawa
iterations. Moreover, while the current analysis of a direct FEM-BEM discretizations
of the Johnson-Nédélec formulation requires some restrictions on the ellipticity (resp.
strong monotonicity constant) in the interior domain, our Uzawa-type solver avoids such

FEM-BEM coupling, adaptivity, Uzawa algorithm.

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