Mixed Finite Volume Method For The Four Order Parabolic Integro-Differential Equations

In this paper, we consider the mixed finite volume element method for the four order parabolic integro-differential equation with the initial-value problems We give the semi-discrete and fully-discrete mixed finite covolume element scheme by quadratic partition, and obtain the optimal error estimates for unknown function in H1-norms, and the error estimates for vorticity in L2-norms by instructing the elliptic projection.Then we simulate the following mixed finite volume element method for the four order parabolic integro-differential equation with the initial-value problems for convecion-dominated diffusion equations The method is combination of characteristic method and mixed finite volume method, obtained the optimal error estimates for unknow function in H1-norms and the error estimates for vorticity in L2-norms, The method not only possess the advantages of mixed finite volume method, for example, high order accuracy,and simplicity of space construction and so on, it also inherits some features of characteristic method: it is stable and can smear sharp front of the solution.