Simple cylindrical and spherical finite elements

Finite element approximations are developed for three-dimensional domains naturally represented in either cylindrical or spherical coordinates. Lines of constant radius, axial length, or angle are used to represent the domain and cast approximations that are natural for these geometries. As opposed to general isoparametric three-dimensional elements generated in conventional parent space, these elements can be evaluated analytically and do not generate geometric discretization error. They also allow for anisotropic material coefficients that are frequently aligned in either cylindrical or spherical coordinates. Several examples are provided that show convergence properties and comparison with analytical solutions of the Poisson equation.