Nonconforming finite element method for a generalized nonlinear Schrödinger equation

Houchao Zhang, Dongyang Shi and Qingfu Li

Applied Mathematics and Computation, 2020, vol. 377, issue C

Abstract: In this paper, an efficient nonconforming finite element method (FEM) is studied with EQ1rot element for a generalized nonlinear Schrödinger equation. First, we prove a novel result of the consistency error estimate with order O(h2) for EQ1rot element which leads to the superconvergent error estimate in broken H1-norm for semi-discrete scheme, while previous work only derive convergent results for this element. Second, a linearized backward Euler scheme is established and a time-discrete system is introduced to split the error into two parts, the temporal error and the spatial error. By using a rigorous analysis for the regularity of the time-discrete system and the proved characters of EQ1rot element, the optimal L2-error estimate is obtained without any time-step restrictions, which leads to the numerical solution can be bounded in L∞-norm by an inverse inequality unconditionally. Then, the supercloseness estimate is arrived at with the above achievements. Third, global superconvergence results are deduced through interpolated postprocessing technique. At last, numerical examples are provided to confirm the theoretical analysis. Here, h is the subdivision parameter, and τ is the time step.

Keywords: Nonconforming finite element method; Generalized nonlinear Schrödinger equation; Linearized backward Euler scheme; Superclose and superconvergence (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320301107

DOI: 10.1016/j.amc.2020.125141

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