hp-Cloud approximation of the Dirac eigenvalue problem: The way of stability

We apply hp-cloud method to the radial Dirac eigenvalue problem. The difficulty of occurrence of spurious values among the genuine eigenvalues is treated. The method of treatment is based on assuming hp-cloud Petrov-Galerkin scheme to construct the weak formulation of the problem which adds a consistent diffusivity to the variational formulation without deforming the equation. The size of the artificially added diffusion term is controlled by a derived stability parameter (τ). The derivation of τ considers the limit behavior of the eigenvalues at infinity. The importance of τ is of being applicable for generic basis functions. This is together with choosing appropriate intrinsic enrichments in the construction of the cloud shape functions.