Analysis And Numerical Tests On Semi-implicit And Implicit Schemes For MEMS Problem

Our aim in this paper is to study the initial and boundary value problem modelling electrostatic Micro-Electromechanical Systems(MEMS):where f(x)describes the permittivity profile of the elastic membrane and A>0 character-izes the applied voltage.We firstly give the mathematical modeling of the problem,and we prove,both for semi-implicit and implicit schemes,that under several assumptions,the solutions are monotonically and pointwise converge to the minimal stable solution of corresponding elliptic partial differential equation.We also give numerical simulations which illustrate the behavior of the solutions with different schemes and different initial conditions,as well as the touchdown phenomenon.