Node and edge element approximation of discontinuous fields and potentials

Compared are node and edge element approximations of vector fields and potentials with continuous tangential components and discontinuous normal components on interface boundaries between different media. For the first order triangular or tetrahedral node elements, the approximation error in the energy norm is O(h^α), 0.25⩽α⩽0.5 (h is the mesh size). Edge elements approximate discontinuous functions without loss in the order of accuracy (i.e., α=1). The relationship between the error of approximation and the error of the Galerkin solution is pointed out