Calculation of fields and their derivatives in highly resonating structures with the FEM

For reliable beam dynamics simulations the precise knowledge of the electromagnetic field distribution within highly resonating structures is mandatory. Numerical models based on the finite element method (FEM) on unstructured grids allow to represent the underlying physical problem up to high accuracy. For the characterization of the three-dimensional fields additionally to the field values also their derivatives are used. In the following work a computationally cheap procedure to calculate the field derivatives in the framework of the FEM is presented.