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ANALYSIS OF DISCRETIZED PARABOLIC PROBLEMS MODELING ELECTROSTATIC MICRO-ELECTROMECHANICAL SYSTEMS

机译:静电微机电系统建模离散抛物面问题分析

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摘要

Our aim in this paper is to study discretized parabolic problems modeling electrostatic micro-electromechanical systems (MEMS). In particular, we prove, both for semi-implicit and implicit semi-discrete schemes, that, under proper assumptions, the solutions are monotonically and pointwise convergent to the minimal solution to the corresponding elliptic partial differential equation. We also study the fully discretized semi-implicit scheme in one space dimension. We finally give numerical simulations which illustrate the behavior of the solutions both in one and two space dimensions.
机译:我们本文的目的是研究静电微机电系统(MEMS)建模的离散抛物线问题。特别是,我们证明了用于半隐式和隐式的半离散方案,即在适当的假设下,解决方案在单调上和将该椭圆偏微分方程的最小解收敛到最小的解决方案。我们还在一个空间维度中研究了完全离散的半隐式方案。我们终于提供了数值模拟,其说明了一个和两个空间尺寸的解决方案的行为。

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    Universite de La Rochelle Laboratoire des Sciences de l'Ingenieur pour l'Environnement UMR CNRS 7356 Avenue Michel Crepeau F-17042 La Rochelle Cedex France;

    Xiamen University School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen Fujian China Universite de Poitiers Laboratoire de Mathematiques et Applications UMR CNRS 7348 Boulevard Marie et Pierre Curie - Teleport 2 F-86962 Chasseneuil Futuroscope Cedex France;

    Laboratoire de Mathematiques et Applications UMR CNRS 7348 Boulevard Marie et Pierre Curie-Teleport 2 F-86962 Chasseneuil Futuroscope Cedex France;

    Xiamen University School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen Fujian China;

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  • 正文语种 eng
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  • 关键词

    Micro-electromechanical systems (MEMS); semi-implicit scheme; implicit scheme; fully discretized scheme; pull-in voltage; minimal solution; numerical simulations;

    机译:微机电系统(MEMS);半隐式方案;隐性方案;完全离散的计划;拉出电压;最小的解决方案;数值模拟;

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