Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation

Journal of Computational Physics, vol. 436, pp. 110165

Abstract

We present an effective adaptive procedure for the numerical approximation of the steady-state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and consists of a combination of a novel adaptive finite element mesh refinement technique, which does not rely on any a posteriori error estimates, and a recently proposed new gradient flow. Numerical tests show that this strategy is able to provide highly accurate results, with optimal convergence rates with respect to the number of degrees of freedom.

Authors 3

1. Pascal Heid corresponding

   University of Oxford · University of Bern

   Affiliation as printed

   Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK

   UNIVERSITY OF BERN

2. Benjamin Stamm Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Applied and Computational Mathematics, Germany

   RWTH Aachen University

3. Thomas P. Wihler

   University of Bern

   Affiliation as printed

   Mathematics Institute, University of Bern, CH-3012 Bern, Switzerland

   UNIVERSITY OF BERN