Uniform $L^\infty$-bounds for energy-conserving higher-order time integrators for the Gross-Pitaevskii equation with rotation

Abstract

In this paper, we consider an energy-conserving continuous Galerkin discretization of the Gross-Pitaevskii equation with a magnetic trapping potential and a stirring potential for angular momentum rotation. The discretization is based on finite elements in space and time and allows for arbitrary polynomial orders. It was first analyzed in [O.