耦合非线性半导体器件问题的低阶不符有限元法超收敛性分析

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-11-14 DOI:10.1016/j.cnsns.2024.108448

Xiangyu Shi , Peng Jian , Dongyang Shi

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引用次数: 0

摘要

针对具有低阶非一致性 EQ1rot 元素的耦合非线性半导体器件问题，开发并研究了线性化解耦完全离散方案。然后，利用其特殊性质：当精确解属于 H3(Ω)时，破碎 H1 准则的一致性误差可达到二阶，仅比其插值误差高一阶，再配合一些适当的方法，如离散导数转移技巧、相邻两时间级差商、数学归纳法等，巧妙地应对了非线性带来的困难，并严格推导出了相关变量的超近似估计。此外，还通过插值后处理方法获得了令人满意的全局超收敛结果。最后，通过一个数值实例验证了理论分析和所提方法的良好性能。

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Superconvergence analysis of low order nonconforming finite element method for coupled nonlinear semiconductor device problem

A linearized decoupled fully discrete scheme is developed and investigated for the coupled nonlinear semiconductor device problem with low order nonconforming

E Q_{1}^{r o t}

element. Then, by use of its special property: the consistency error in the broken

H^{1}

-norm can reach to second order when the exact solutions belong to

H^{3} (Ω)

, just one order higher than its interpolation error, together with some proper approaches such as the discrete derivative transfer trick, difference quotient between two adjacent time levels, mathematics induction method and so on, the difficulty caused by the nonlinearity is ingeniously coped with, and the superclose estimates about the related variables are derived rigorously. In addition, the satisfactory global superconvergence results are obtained through the interpolation postprocessing approach. Finally, a numerical example is presented to validate the theoretical analysis and the good performance of the proposed method.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.