Adaptive finite-element mesh generation for optimization problems

For several optimization problems, occurring in electrical engineering applications, an underlying field problem is treated by means of a finite-element scheme. The finite-element mesh has to be set up in such a way that the results attain a certain desired accuracy. However, in case of optimization problems, the criterion for mesh accuracy is not the largest error of the calculated field in the whole domain, but rather the error on the cost functional, which is going to be minimized. In this paper, a method for adaptive mesh generators, suitable for optimization problems, is presented, making use of Lagrange multiplier information.