An ultraweak-local discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations

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dc.citation.firstpage1725en_US
dc.citation.issueNumber5en_US
dc.citation.journalTitleESAIM: Mathematical Modelling and Numerical Analysisen_US
dc.citation.lastpage1754en_US
dc.citation.volumeNumber58en_US
dc.contributor.authorWang, Qien_US
dc.contributor.authorZhang, Luen_US
dc.contributor.orgKen Kennedy Instituteen_US
dc.date.accessioned2024-10-29T14:11:23Zen_US
dc.date.available2024-10-29T14:11:23Zen_US
dc.date.issued2024en_US
dc.description.abstractThis paper proposes and analyzes a fully discrete scheme for nonlinear biharmonic Schrödinger equations. We first write the single equation into a system of problems with second-order spatial derivatives and then discretize the space variable with an ultraweak discontinuous Galerkin scheme and the time variable with the Crank–Nicolson method. The proposed scheme proves to be computationally more efficient compared to the local discontinuous Galerkin method in terms of the number of equations needed to be solved at each single time step, and it is unconditionally stable without imposing any penalty terms. It also achieves optimal error convergence in L2 norm both in the solution and in the auxiliary variable with general nonlinear terms. We also prove several physically relevant properties of the discrete schemes, such as the conservation of mass and the Hamiltonian for the nonlinear biharmonic Schrödinger equations. Several numerical studies demonstrate and support our theoretical results.en_US
dc.identifier.citationWang, Q., & Zhang, L. (2024). An ultraweak-local discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations. ESAIM: Mathematical Modelling and Numerical Analysis, 58(5), Article 5. https://doi.org/10.1051/m2an/2024023en_US
dc.identifier.digitalm2an230135en_US
dc.identifier.doihttps://doi.org/10.1051/m2an/2024023en_US
dc.identifier.urihttps://hdl.handle.net/1911/117964en_US
dc.language.isoengen_US
dc.publisheredp Sciencesen_US
dc.rightsExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license. Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleAn ultraweak-local discontinuous Galerkin method for nonlinear biharmonic Schrödinger equationsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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