The finite volume element methods for Poisson equation based on Adini's element

In this paper, we construct and analyze the finite volume element scheme based on Adini's element for Poisson equation, choosing trial and test spaces as the Adini's finite element space and the piecewise linear function space respectively. Optimal order error estimates in H1 and L2 norms are derived. In addition, the global and locally pointwise superconvergence estimates are also discussed. Lastly, a numerical experiment is carried out, which confirms some results of theoretical analysis.