Finite Element Methods for Microelectromechanical Systems

Abstract: The stationary Joule heating problem is a crucial multiphysical problem for many microelectromechanical (MEMS) applications. In our paper, we derive a finite element method for this problem and introduce iterative solution-techniques to compute the numerical simulation. Further we construct an adaptive algorithm for mesh refinement based on a posteriori error estimation.Finally, we present two numerical tests: convergences analysis of different iterative methods for distinct materials which are classified by electrical conductivities, and a test of the new adaptive refinement algorithm. All the numerical implementations have been done in MATLAB.