A novel finite element discretization of domains with spheroidal geometry

Abstract

We describe and analyze a new finite element discretizations for domains with spheroidal geometry. In particular, we describe how the method can be used to approximate solutions as well as eigenvalues and eigenfunctions of partial differential equations posed on the sphere, ellipsoidal shell, and cylindrical shell. These novel, so-called, “radially projected finite elements” are particularly attractive for numerical simulations since the resulting finite element discretization is “logically rectangular” and may be easily implemented or incorporated into existing finite element codes.