One Dimension Fourth-order Finite Volume Method Based On The Lobatto-Gauss Constructure

In this paper, we designed a kind of one dimension fourth-order finite volume methodbased on the Lobatto-Gauss constructure: The trial function is taken as the forth order La-grange interpolated function associated with the nodes, which is the zero points of the fifthLobatto polynomial on the partition element, and the derivative super-convergent pointsof the interpolated function as dual partition nodes. The stability and convergence for themethod are obtained: We proved the positive definiteness of the bilinear form a(·, Π andthe method has optimal convergence orders of H~1; It was given the weak estimate of the bilin-ear form, then we proved the optimal convergence orders of L~2norm; the super-convergenceof numerical derivatives at the dual partition nodes was discussed. Finally, the numerical...