  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 the maximal
angle condition holds. Therefore, optimal order of convergence can be shown.
Moreover, an appropriate scaling 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 is evolving in the course of the optimization procedure.

Numerical Analysis