Mixed Finite Volume Method Based On Triangle Mesh For The Four Order Parabolic Integro-Differential Equations

In this paper, we consider the mixed finite volume element method based on tri-angle mesh 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 based on triangle mesh, obtain the optimal error estimates for unknown function inH1-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 advantagesof mixed finite volume method, for example, high order accuracy,and simplicity ofspace construction and so on, it also inherits some features of characteristic method:it is stable and can smear sharp front of the solution.