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A challenging difficulty in solving the radial Dirac eigenvalue problemnumerically is the presence of spurious (unphysical) eigenvalues among thecorrect ones that are neither related to mathematical interpretations nor tophysical explanations. Many attempts have been made and several numericalmethods 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 aFEM approach, this work can be regarded as a first promising scheme to solvethe spuriousity problem completely. Our approach is based on an appropriatechoice of trial and test functional spaces. We develop a Streamline UpwindPetrov-Galerkin method (SUPG) to the equation and derive an explicit stabilityparameter.

Stabilized Finite Element Method for the Radial Dirac Equation