L2 error estimate of the finite volume element methods on quadrilateral meshes

In this paper the optimal L2 error estimates of the finite volume element methods (FVEM) for Poisson equation are discussed on quadrilateral meshes. The trial function space is taken as isoparametric bilinear finite element space on quadrilateral partition, and the test function space is defined as piecewise constant space on dual partition. Under the assumption that all elements on quadrilateral meshes are O(h2) quasi-parallel quadrilateral elements, we prove convergence rate to be O(h2) in L2 norm.