Superconvergence For Quadratic Finite Volume Method On Rectangular Meshes

In this paper, by use of simple a?ne transformation, we construct and analyze thefinite volume methods on eight nodes and nine nodes on rectangular networks for Poissonequations. In Chapter 1, we introduce the ordinary development history of the finitevolume methods, and also the recent search progress of the relevant issues. In Chapter2, on the base of the known results in literature [9], through the seriously detailded com-putions. The pointswise asymptotic expansions of the biquadratic finite volume elementand derivatives superconvergence result is firstly derived in this thesis, when the Gausspoints are the dual subdivision nodes. In Chapter 3, we have the eight nodes finite volumeschemes, and obtain the coercivity of the bilinear form and H1 error estimates , when theα(0.005 <α< 0.446)is the dual subdivision nodes.In addition, the H1 error estimates isin step with the nine points condition in literature [9].