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Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.ORCID-id: 0000-0002-6432-5504
2017 (Engelska)Ingår i: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 27, nr 11, s. 2147-2184Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
World Scientific Publishing Co. Pte Ltd , 2017. Vol. 27, nr 11, s. 2147-2184
Nyckelord [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
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
URN: urn:nbn:se:kth:diva-218865DOI: 10.1142/S0218202517500415ISI: 000408991400005Scopus ID: 2-s2.0-85026383268OAI: oai:DiVA.org:kth-218865DiVA, id: diva2:1176411
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QC 20180122

Tillgänglig från: 2018-01-22 Skapad: 2018-01-22 Senast uppdaterad: 2018-01-22Bibliografiskt granskad

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