Discontinuous Volume Method For Parabolic Type Intergo-differential Equations

In this paper, we consider discontinuous finite volume method on triangular grids for the linear Sobolev equationsThe method does not require continuity of the approximation functions across the interelement boundary conditions, which makes it easy to construct the space. Due to the advantages of a high order of accuracy, high parallelizability and so on, the study of discontinuous finite volume method has been an effective method of dealing with the problem. In this chapter, by making the numerical analysis, we obtain the optimal error estimates of L2-norm and (?)·(?)1,h-norm about the unknown function.Secondly, we simulate the following psendparabolic intergo-differential equa-tions by discontinuous finite volume method in a similar way. By defining the Sobolev-Volterra projection of this problem, we can obtain the the optimal error estimates of (?)·(?)1,h-norm about the unknown function. At last, we simulate the following linear parabolic problem by discontinuous mixed volume method based on Zhang Xiaoxiao's work about advection-diffusion problem. In this chapter we propose the semi discretization discontinuous mixed volume procedures for this problem, and we obtain the optimal error estimate about the unknown function by this method.