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- Title
Analysis of discretized parabolic problems modeling electrostatic micro-electromechanical systems.
- Authors
Cherfils, Laurence; Miranville, Alain; Peng, Shuiran; Xu, Chuanju
- Abstract
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.
- Publication
Discrete & Continuous Dynamical Systems - Series S, 2019, Vol 12, Issue 6, p1601
- ISSN
1937-1632
- Publication type
Academic Journal
- DOI
10.3934/dcdss.2019109