Computational and Applied Mathematics seminar

Abstract: In this talk, we present a lowest order Raviart-Thomas finite element discretization that provides guaranteed lower bounds on the ground state energy of the nonlinear Gross-Pitaevskii problem. We emphasize that due to their conformity, classical discretization methods such as the P¹ or Q¹ finite element methods can only provide upper bounds on the ground state energy. Furthermore, we establish an a priori error analysis for the Raviart-Thomas discretization of the Gross-Pitaevskii problem. Optimal convergence rates are shown for the primary and dual variables as well as for the eigenvalue and energy approximations.