[Back]

M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius:
"Convergence of adaptive FEM-BEM coupling driven by residual-based error estimators";
Poster: TCSE Vienna Workshop 2012, Trends in Computational Science and Engineering, Wien; 02-13-2012 - 02-14-2012.

A broad range of physical problems can be described as transmission problems. Efficient methods for solving these problems are FEM-BEM couplings together with an adaptive mesh-refinement, because the accuracy of the computed approximation hinges on the singularities of the given data and / or on the singularities of the unknown exact solution. In contrast to a uniform strategy, adaptive mesh-refinement aims to resolve these singularities effectively.
Here, we use the Johnson-Nédélec FEM-BEM coupling and a certain residual-based error estimator to steer the adaptive mesh-refinement.
We show that this estimator fulfills a reduction property, which together with elementary calculus proves that the Galerkin solutions obtained from the adaptive algorithm converge to the exact solution.
Finally, the rigorous mathematical theory is underlined by a numerical
experiment: We consider the computation of the magnetostatic potential, which is a bottleneck in most micromagnetic simulations.

http://publik.tuwien.ac.at/files/PubDat_206759.pdf