Some recent advances on vertex centered finite volume element methods for elliptic equations

In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic finite volume schemes. Then we present our recent advances on finite volume schemes of arbitrary order. For each scheme, we first explain its construction and then perform its error analysis under both HI and L2 norms along with study of superconvergence properties.

In this paper,we report our recent advances on vertex centered fnite volume element methods(FVEMs)for second order partial diferential equations(PDEs).We begin with a brief review on linear and quadratic fnite volume schemes.Then we present our recent advances on fnite volume schemes of arbitrary order.For each scheme,we frst explain its construction and then perform its error analysis under both H1and L2norms along with study of superconvergence properties.