Conservative Conforming and Nonconforming VEMs for Fourth Order Nonlinear Schrödinger Equations with Trapped Term
Year: 2024
Author: Meng Li, Jikun Zhao, Zhongchi Wang, Shaochun Chen
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 454–499
Abstract
This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrödinger equations with trapped term. We mainly consider three types of virtual elements, including $H^2$ conforming virtual element, $C^0$ nonconforming virtual element and Morley-type nonconforming virtual element. The fully discrete schemes are constructed by virtue of virtual element methods in space and modified Crank-Nicolson method in time. We prove the mass and energy conservation, the boundedness and the unique solvability of the fully discrete schemes. After introducing a new type of the Ritz projection, the optimal and unconditional error estimates for the fully discrete schemes are presented and proved. Finally, two numerical examples are investigated to confirm our theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2209-m2021-0038
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 454–499
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 46
Keywords: $H^2$ conforming virtual element $C^0$ nonconforming virtual element Morley-type nonconforming virtual element Nonlinear Schrödinger equation Conservation Convergence.
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