Superconvergence And Asymptotic Expansions For Bilinear Finite Volume Element

Finite volume method is one of important numerical methods for discretizingpartial di?erential equations. The isoparametric bilinear finite volume elementmethod is an well-known one widely used in many fields, such as computational?uid mechanics. The saturated order of error and the superconvergence in theaverage sense have been obtained by some people for elliptic equations. The point-wise asymptotic expansions of the isoparametric bilinear finite volume elementis firstly derived on rectangle grids for the Laplace Problem with the Dirichletboundary in this thesis . With the asymptotic expansions, a high accuracy com-bination formula for the approximate derivatives in pointwise is achieved. Therequirement for the regularity of solution is more weak than that in the literature[32]. Finally, numerical examples verify theoretical results.