Stabilized finite element method for the radial Dirac equation
Artikel i vetenskaplig tidskrift, 2013

A challenging difficulty in solving the radial Dirac eigenvalue problem numerically is the presence of spurious (unphysical) eigenvalues, among the genuine 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 the finite element method (FEM), the finite difference method, 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 spuriosity problem com- pletely. Our approach is based on an appropriate choice of trial and test function spaces. We develop a Streamline Upwind Petrov–Galerkin method to the equation and derive an explicit stability parameter.

Finite element scheme

spurious solutions

Cubic Hermite functions


Dirac operator

Spurious eigenvalue


eigenvalue problems



Hasan Almanasreh

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Sten Salomonson

Göteborgs universitet

Nils Svanstedt

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Journal of Computational Physics

0021-9991 (ISSN) 1090-2716 (eISSN)

Vol. 236 426-442


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