A Study Of Mixed Finite Element Two-grid Method For Cahn-Hilliard Equation With Constant And Variable Coefficients

In modern computing science,it is especially important to seek and construct the appropriate numerical method.The advantage of mixed finite element method is that by introducing new variables,the original high-order equation is transformed into two low order equations,thereby reducing the smooth conditions of finite element space.The two-grid method is a common numerical method,and we use two-grid subspace to solve the complex problem,which can be solved by solving the simple problem of the fine grid and effectively reduced the computational cost in coarse grid.In this paper,based on the advantages of above two methods and the difficulties of the research,we propose and analyze a method of mixed finite element and new two-grid method to solve the fourth-order constant coefficient and variable coefficient equations with the nonlinear item.The two-grid method is mainly used to solve the problem of high computing cost of nonlinear term.For the term of the fourth partial derivative in the equation,since it is difficult to solve the higher order term,we consider using the mixed finite element method to introduce new variable to transform it into two second-order equations.In this paper,stability analysis and convergence analysis of this numerical method are proved.Finally,the consistency of numerical results and theoretical analysis is verified by numerical experiment.