Highly accurate 3D field gradient computation using local post-solving

To enhance the accuracy of finite element based computations of field quantities and their derivatives, a post-solving technique with superconvergent properties is presented. This technique uses an analytical expression for the magnetic field potential inside a closed region. The coefficients of the analytical expression are evaluated using a FE solution as boundary condition. All second derivatives of the analytical expression are calculated, leading to values for the flux density B and its derivatives. These values are highly accurate, even when based upon a FE solution. As an example, the (edge) write gradient in a notch write head is evaluated.