  In this work we will treat the spurious eigenvalues obstacle that appears in
the computation of the radial Dirac eigenvalue problem using numerical methods.
The treatment of the spurious solution is based on applying Petrov-Galerkin
finite element method. The significance of this work is the employment of just
continuous basis functions, thus the need of a continuous function which has a
continuous first derivative as a basis, as in [ALMAN,ALMANA,ALMA], is no longer
required. The Petrov-Galerkin finite element method for the Dirac eigenvalue
problem strongly depends on a stability parameter, $\tau$, that controls the
size of the diffusion terms added to the finite element formulation for the
problem. The mesh-dependent parameter $\tau$ is derived based on the given
problem with the particular basis functions.
