Efficient Numerical Simulation for the Quasilinear Elliptic Problems

With the rapid development of computing power, some efficient numerical methods are presented. In this paper, expanded mixed finite element method is introduced to solve the quasilinear elliptic problems. This method expands the traditional mixed finite element method in the sense that three variables are explicitly treated simultaneously. Existence and uniqueness of the discrete approximation are demonstrated. L2 2-error estimates for three variables are presented. Numerical examples are carried out to validate the theoretical analysis.