Splitting Mixed Finite Volume Element Method For Two Kinds Of Evolution Equations

In this thesis,splitting mixed finite volume element method for two kinds of evolution equations is studied by combining the splitting idea with the mixed finite volume element method.In the process of numerical calculation,this method can first solve the numer-ical solution of one variable,and then solve the second variable by using the numerical solution first variable,this splitting idea can reduce the scale of algebraic equations and the computational time.In Chapter 1,the historical background and development of mixed finite volume element method are briefly introduced.In Chapter 2 and Chapter 3,splitting mixed finite volume element methods for a kind of convection diffusion equation and a kind of viscoelastic wave equation are studied respectively.By introducing the transfer operator ?_h which maps the lowest order Raviart-Thomas finite element space into the test func-tion space,semi-discrete and fully-discrete mixed finite volume element schemes for two kinds of evolution equations are constructed,the existence and uniqueness of semi-discrete scheme are proved,and optimal order error estimates for semi-discrete and fully-discrete schemes are derived.Finally,numerical examples of two kinds of model equations are given to illustrate the effectiveness.