Symmetric Discontinuous Finite Volume Element Methods For Parabolic Integro-Differential Equations

The finite volume element method is a discretization technique, in general case the coefficient matrix of its linear system is not symmetric. This has resulted in a single solution method, and operation procedure of the space is large. In view of this, we study symmetrical discontinuous volume element method. By symmetrizing the bilinear forms and then correcting the scheme, we obtain a kind of symmetric modified finite volume element method.In this paper, firstly the following initial boundary value problem (?) is simulated by a new method called symmetric modified discontinuous finite volume element method. By correcting the discontinuous finite volume element method, we obtain a kind of symmetric modified discontinuous finite volume element method for elliptic problem. Our analysis shows that the new method not require continuity of the approximation functions across the interelement boundary conditions, which makes it easy to construct the space. And the method also has the advantages of a high order of accuracy, high parallelizability and so on. In this paper, the semi -discrete and fully discrete symmetric discontinuous finite volume modules are given respectively, And by defining the Sobolev projection of the problem, we obtain the optimal error estimates of L2-norm and |||· |||1,h-norm about the unknown function;Finally, the numerical experiments support the theoretical analysis results.