  A challenging difficulty in solving the radial Dirac eigenvalue problem
numerically is the presence of spurious (unphysical) eigenvalues among the
correct ones that are neither related to mathematical interpretations nor to
physical explanations. Many attempts have been made and several numerical
methods have been applied to solve the problem using finite element method
(FEM), finite difference method (FDM), or other numerical schemes.
Unfortunately most of these attempts failed to overcome the difficulty. As a
FEM approach, this work can be regarded as a first promising scheme to solve
the spuriousity problem completely. Our approach is based on an appropriate
choice of trial and test functional spaces. We develop a Streamline Upwind
Petrov-Galerkin method (SUPG) to the equation and derive an explicit stability
parameter.
