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Stabilized finite element method for the radial Dirac equation

Hasan Almanasreh (Institutionen för matematiska vetenskaper) ; Sten Salomonson ; Nils Svanstedt (Institutionen för matematiska vetenskaper)
Journal of Computational Physics (0021-9991). Vol. 236 (2013), p. 426-442.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Dirac operator, Finite element scheme, Spurious eigenvalue, Cubic Hermite functions, Petrov-, eigenvalue problems, spurious solutions, origin, orbatsch

Denna post skapades 2013-03-19. Senast ändrad 2013-03-26.
CPL Pubid: 174826


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