Guaranteed lower energy bounds for the Gross-Pitaevskii problem using mixed finite elements

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 $\mathcal P^1$ or $\mathcal Q^1$ 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.

numerical analysisoptimization and control

Audience: researchers in the topic

CAM seminar

Series comments: Online streaming via zoom on exceptional cases if requested. Please contact the organizers at the latest Monday 11:45.