Essential arithmetic for evaluating three dimensional vector finite element interpolation schemes

The author extends previous work to discretizations, over tetrahedral and hexahedral meshes, of functionals which often arise in the analysis of magnetoquasistatic problems. For natural boundary conditions, exact formulae for the number of degrees of freedom and the number of nonzero entries in the stiffness matrix are given in terms of the number of nodes in the mesh, the number of elements, the number of boundary nodes, and the Euler characteristic. From this, explicit formulae for the number of FLOPS (floating point operations) per conjugate gradient iteration are given for node- and edge-based vector interpolation on hexahedral and tetrahedral meshes. Thus, formulae for quantities required for the comparison and validation of finite element codes are given.<>