New Higher Order Two-dimensional Singular Elements for FEM and MOM Applications

A procedure to obtain in a unified and consistent manner singular vector bases complete to arbitrarily high order has been obtained for curved triangular and quadrilateral elements. These vector basis functions are fully compatible with the standard, high-order regular vector functions used in adjacent elements. The curl (divergence) conforming singular functions guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modelling of the curl (divergence), and removal of spurious modes (solutions).