A Modified Characteristics Finite Element Method for the Electroneutral Micro-Fluids

Abstract

In this paper, a numerical method for the electroneutral micro-fluids based on the finite element method will be given. In order to deal with the non-linearity of the equation, the modified characteristics method will be used to deal with the temporal derivative term and the convective term. In this way, the non-linear equation can be linearized. Then, we will give the unconditional stability and optimal error estimation. At last, some numerical results are given to show the effectiveness of our method. From the stability analysis we can see that the method is unconditionally stable. The numerical results show that our method is robust.