Mixed finite elements for the Gross-Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound
Artikel i vetenskaplig tidskrift, 2024

We establish an a priori error analysis for the lowest-order Raviart-Thomas finite element discretization of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence rates are obtained for the primal and dual variables as well as for the eigenvalue and energy approximations. In contrast to conforming approaches, which naturally imply upper energy bounds, the proposed mixed discretization provides a guaranteed and asymptotically exact lower bound for the ground state energy. The theoretical results are illustrated by a series of numerical experiments.

Gross-Pitaevskii eigenvalue problem

lower bounds

a priori error analysis

mixed finite elements

Författare

Dietmar Gallistl

Friedrich-Schiller-Universität Jena

Moritz Hauck

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Yizhou Liang

Univ Augsburg

Daniel Peterseim

Univ Augsburg

IMA Journal of Numerical Analysis

0272-4979 (ISSN) 1464-3642 (eISSN)

Vol. In Press

Undersökning av membran-fouling vid tvärflöde filtrering av vedkomponenter

Knut och Alice Wallenbergs Stiftelse, 2019-04-15 -- 2023-11-15.

Knut och Alice Wallenbergs Stiftelse, 2014-03-01 -- 2019-02-28.

Ämneskategorier

Beräkningsmatematik

DOI

10.1093/imanum/drae048

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Senast uppdaterat

2024-09-26