Numerical analysis of superconductivity

Motivated by the superconductivity, we are interested in the fundamental state of the Schorodinger operator with magnetic field. In this paper, we propose a numerical approach based on the finite elements method to determine the bottom of the spectrum of this operator in general domains. We improve the numerical results by using mesh-refinement techniques based on a posteriori error estimators developed elsewhere. We also look at the monotonicity of the bottom of the spectrum in an angular sector according to the angle to complement the theorical. study of Bonnaillie (C.R. Acad. Sci. Paris, Ser. I 336 (2) (2003) 135-140).