Discontinuous Finite Volume Element Method For Sobolev Equation With Convection

In this paper,we frstly consider discontinuous fnite volume method on trian-gular grids for the Sobolev equation with convectio nThis method does not require continuity of the approximation functions across theinterelement boundary conditions, which makes it easy to construct the space.Andthe method also has the advantages of a high order of accuracy, high parallelizabilityand so on. In this paper, by making the numerical analysis, we obtain the optimalerror estimates of L2-norm and|||·|||1,h-norm about the unknown function.Secondly, we introduce an upwind discontinuous fnite volume method on tri-angular grids for the above problem. This method combines the upwind techniquewith the discontinuous fnite volume method which is introduced by Ye Xiu. Byusing the upwind technique, we can eliminate some combination of nonphysical os-cillation and excessive numerical dispersion. Furthermore, we obtain the L2-normand|||·|||1,h-norm.Lastly, according to numerical examples, we confrm the correction of the con-vergence results.