This paper used the finite element method and the finite difference method to solve the two-dimensional variable coefficient elliptic boundary value problem. It get the corresponding error analysis, and numerical simulation, the process requires application software MATLAB programming. Results show that they compared to the two methods and finite element the procedure is simple. The numerical results have the high accuracy and good stability. A two-dimensional variable coefficient elliptic partial differential equation is studied. This paper studies application of genetic algorithm to solve the genetic algorithm. A population search strategy basically does not depend on the knowledge of space or other auxiliary information, and the change rules of probability to control the search direction. It get the corresponding error analysis, and numerical simulation is carried out, the process of programming also requires the application of MATLAB software; results show that the nonlinear optimization method genetic algorithm does not need to choose the initial values of the results with high precision.