COMPUTATION OF THE EIGENPAIRS FOR A LINEAR DIFFERENTIAL OPERATOR USING A VARIATIONAL APPROXIMATION WITH FINITE ELEMENTS AND NUMERICAL QUADRATURE

This paper is about an eigenvalue problem for a Schrodinger operator with constant magnetic field, coming from the Ginzburg-Landau theory and the supraconductivity of some materials. For the numerical computation we use a finite element method with numerical quad-rature. The existence of solutions for the variational problem has been established. Numerical results are about the localisation of the fundamental states under constant magnetic fields for different domains (disc, ellipse, square and hexagon). They are in agreement with the physical theory.