Spurious modes in quadrilateral and triangular edge elements

Quadrilateral and triangular edge elements are known to eliminate spurious modes from the computed spectrum of electromagnetic cavities. Various features of the elements have been cited as the reason. In this paper, the lack of continuity of the normal part of the field is shown to be important in all cases. On the other hand, none of the elements have truly divergence-free basis functions, so solenoidality does not play a part. Finally, mixed-order approximation (the use of different polynomial orders for representing the variation of the field in the direction of the vector, and in the other directions) is shown to be necessary for quadrilaterals, but not for triangles. All of these results can be understood in terms of the relative size of the irrotational subspace of the trial function space.