Combined tangential-normal vector elements for computing electric and magnetic fields

A direct method for computing electric and magnetic fields in two dimensions is developed. This method determines both the fields and fluxes directly from Maxwell´s curl and divergence equations without introducing potential functions. This allows both the curl and the divergence of the field to be set independently in all elements. The technique is based on a novel type of vector finite element that simultaneously interpolates to the tangential component of the electric or magnetic flux. Continuity conditions are imposed across element edges. This guarantees the continuity of the field and flux at the mid-point of each edge, and its also guarantees that for all edges the average values of the tangential component of the field and of the normal component of the flux are identical