Discontinuous Space-time Finite Volume Method For Parabolic Problems

In this paper, we consider the Finite Volume element method for continuous inspace but discontinuous in time for the linear parabolic equationsThis method not only has the advantages of a high order of accuracy, computingeasily,and can keep the local conservation property,but also makes it easy to changetime step.It deals with the spatial and temporal variables conformably.Thus highorders of accuracy in both directions are achieved. In this chapter,by making thenumerical analysis,we obtain the optimal error estimates of L∞(L2)norm about theunknown function.Secondly,we consider the discontinuous space-time Finite volume element methodThis method deals with the spatial and the temporal variables conformably.Thushigh orders of accuracy in both directions are achieved.It does not require continuityof the approximation functions across the interelement boundary conditions, which makes it easy to construct the space. In this chapter,by making the numericalanalysis,we obtain the optimal error estimates of L∞(L2)norm about the unknownfunction.At last,base on the discontinuous finite volume method for the linear Sobolevequations.We consider the backward Euler fully discrete discontinuous finite volumeelement scheme for the Sobolev equationNumerical analysis shows that we can obtain the optimal error estimates of L2-normand|||·|||1,h-norm about the unknown function by this method.