L2 error estimates and superconvergence of the finite volume element methods on quadrilateral meshes

This paper is concerned with the finite volume element methods on quadrilateral mesh for second-order elliptic equation with variable coefficients. An error estimate in L2 norm is shown on the quadrilateral meshes consisting of h2-parallelograms. Superconvergence of numerical solution is also derived in an average gradient norm on h2-uniform quadrilateral meshes. Numerical examples confirm our theoretical conclusions.