Analysis and application of finite volume element methods to a class of partial differential equations

The finite volume element (FVE) methods for a class of partial differential equations are discussed and analyzed in this paper. The new initial values are introduced in the finite volume element schemes, and we obtain optimal error estimates in Lp and W1,p (2⩽p⩽∞) as well as some superconvergence estimates in W1,p (2⩽p⩽∞). The main results in this paper perfect the theory of the finite volume element methods.