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Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0002-6432-5504
2017 (English)In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 27, no 11, p. 2147-2184Article in journal (Refereed) Published
Abstract [en]

This paper analyzes the numerical solution of a class of nonlinear Schrödinger equations by Galerkin finite elements in space and a mass and energy conserving variant of the Crank-Nicolson method due to Sanz-Serna in time. The novel aspects of the analysis are the incorporation of rough, discontinuous potentials in the context of weak and strong disorder, the consideration of some general class of nonlinearities, and the proof of convergence with rates in L∞(L2) under moderate regularity assumptions that are compatible with discontinuous potentials. For sufficiently smooth potentials, the rates are optimal without any coupling condition between the time step size and the spatial mesh width.

Place, publisher, year, edition, pages
World Scientific Publishing Co. Pte Ltd , 2017. Vol. 27, no 11, p. 2147-2184
Keywords [en]
Bose-Einstein condensates, Crank-Nicolson, finite elements, Nonlinear Schrödinger equation, Control nonlinearities, Finite element method, Galerkin methods, Numerical methods, Coupling condition, Dinger equation, Discontinuous potentials, Einstein condensate, Galerkin approximations, Galerkin finite elements, Numerical solution, Regularity assumption, Nonlinear equations
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-218865DOI: 10.1142/S0218202517500415ISI: 000408991400005Scopus ID: 2-s2.0-85026383268OAI: oai:DiVA.org:kth-218865DiVA, id: diva2:1176411
Note

QC 20180122

Available from: 2018-01-22 Created: 2018-01-22 Last updated: 2018-01-22Bibliographically approved

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Henning, Patrick

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