Abstract
We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and a maximum angle condition holds. Therefore, optimal order of convergence can be shown. Moreover, it can be shown that an appropriate choice of the basis functions yields an optimal condition number of the stiffness matrix. The method is applied to an optimal design problem for an electric motor where the interface between different materials evolves in the course of the optimization procedure.
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Acknowledgements
The authors gratefully acknowledge the Austrian Science Fund (FWF) for the financial support of their work via the Doctoral Program DK W1214 (project DK4) on Computational Mathematics. They also thank the Linz Center of Mechatronics (LCM), which is a part of the COMET K2 program of the Austrian Government, for supporting their work.
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Gangl, P., Langer, U. (2018). A Local Mesh Modification Strategy for Interface Problems with Application to Shape and Topology Optimization. In: Langer, U., Amrhein, W., Zulehner, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-75538-0_14
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DOI: https://doi.org/10.1007/978-3-319-75538-0_14
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