Superconvergent biquadratic finite volume element method for two-dimensional Poisson’s equations

In this paper, a kind of biquadratic finite volume element method is presented for two-dimensional Poisson’s equations by restricting the optimal stress points of biquadratic interpolation as the vertices of control volumes. The method can be effectively implemented by alternating direction technique. It is proved that the method has optimal energy norm error estimates. The superconvergence of numerical gradients at optimal stress points is discussed and it is proved that the method has also superconvergence displacement at nodal points by a modified dual argument technique. Finally, a numerical example verifies the theoretical results and illustrates the effectiveness of the method.