Symmetric Modified Discontinuous Finite Volume Element Methods For Elliptic And Parabolic Problems

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 elliptic 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, 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 parabolic problem by symmetric modified discontinuous finite volume element method. In this paper we propose the semi and whole discretization symmetric modified discontinuous finite volume procedures for this problem, and we obtain the optimal error estimates of L2-norm and|||·||| 1,h-norm about the unknown function.