Numerical Analysis Of Discontinuous Finite Volume Element Method For Two Kinds Of Evolution Equations

Firstly,in this paper,we consider discontinuous finite volume element method forlinear parabolic integro-diferential equationsDue to discontinuous finite volume element method with high precision, high par-allelizability, easy to construct the space and many other benefits, therefore themethod proposed has been favored by many scholars. In this article we give a semi-discrete linear parabolic integro-diferential equation of discontinuous finite volumeelement, Ritz-Volterra projection, and by making the theoretical analysis, we obtainthe optimal error estimate of L2model and H1model of discrete discontinuous finitevolume element format solution.Secondly, method on the basis of chapter II of this article, we simulate the following nonlinear hyperbolic equationsby discontinuous finite volume element method. we give a semi-discrete nonlinearhyperbolic equation of discontinuous finite volume element, define the problem ofelliptical projection, and gives its approximation properties. At the same time, bymaking the theoretical analysis, we obtain the optimal error estimate of L2modeland H1model of discrete discontinuous finite volume element format solution.