A preconditioned MINRES method for the coupling of mixed-FEM and
BEM in some nonlinear problems
Gabriel N. Gatica, Norbert Heuer
SIAM J. Sci. Comput. 24 (2), 572-596, 2002.
We provide an efficient solution procedure for the linearized Galerkin schemes arising from
the combined use of mixed finite elements and boundary elements to solve nonlinear problems. As
a model, we consider a nonlinear-linear transmission problem appearing in electromagnetism and
steady heat conduction. Since the corresponding continuous and discrete variational formulations
become nonlinear two-fold saddle point problems (also called dual-dual formulations), we
propose to apply Newton's method to the Galerkin schemes, thus yielding linear systems with the
same dual-dual structure. Hence, we follow previous works on this kind of operator equation and
derive a preconditioned minimum residual method that guarantees a bounded number of
iterations (independent of the mesh size) to solve these systems.