Quenching Behavior of a Higher-Order Electrostatic Microelectromechanical System

Higher-order nonlinear effects induced by electrostatic coupling, large-deflection deformation and bending stiffness substantially alter the quenching evolution of elastic membranes in practical electrostatic MEMS devices. This paper investigates a higher-order electrostatic MEMS model with nonlinear diffusion power m∈N+. Stronger electrostatic nonlinearities modify quenching behavior, and the parity of m significantly influences the construction of discrete schemes. We first construct a semidiscrete scheme for odd-power cases, while the even-power cases require a fully discrete scheme with adaptive time-stepping near the quenching time. For both schemes, we establish stability and convergence of the corresponding discrete quenching solutions. Finally, numerical simulations corroborate the theoretical findings and provide intuitive illustrations of the quenching behavior, clearly demonstrating how higher-order nonlinearities affect the evolution of quenching, with insights for defining safe operating ranges and mitigating device failure.