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The finite element method for the time-dependent gross-pitaevskii equation with angular momentum rotation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2017 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 55, no 2, 923-952 p.Article in journal (Refereed) Published
Abstract [en]

We consider the time-dependent Gross Pitaevskii equation describing the dynamics of rotating Bose Einstein condensates and its discretization with the finite element method. We analyze a mass conserving Crank-Nicolson-type discretization and prove corresponding a priori error estimates with respect to the maximum norm in time and the L-2- and energy-norm in space. The estimates show that we obtain optimal convergence rates under the assumption of additional regularity for the solution to the Gross Pitaevskii equation. We demonstrate the performance of the method in numerical experiments.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2017. Vol. 55, no 2, 923-952 p.
Keyword [en]
Bose-Einstein condensate, finite element method, Gross-Pitaevskii equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-209356DOI: 10.1137/15M1009172ISI: 000401780500020Scopus ID: 2-s2.0-85018994984OAI: oai:DiVA.org:kth-209356DiVA: diva2:1112358
Funder
Swedish Research Council, 621-2011-3795 2016-03339
Note

QC 20170620

Available from: 2017-06-20 Created: 2017-06-20 Last updated: 2017-06-20Bibliographically approved

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  • apa
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