Symmetric second order edge elements for triangles and tetrahedra

A new type of second order edge elements for simplexes (triangles and tetrahedra) is proposed. The element is geometrically symmetric and the shape functions are orthogonal to each other in the integrals of the tangential components on edges. The number of nodes and edges are 14 and 24 in a tetrahedral element. The proposed elements are validated by eigenmode calculations in a cavity using newly developed method to solve eigenvalue problems with large matrices. Highly accurate eigenvalues are calculated using the elements.