LAUSR

In this paper, we construct and analyze a nonconforming finite volume method (FVM) for solving the elliptic boundary value problems on quadrilateral meshes: the hybrid Wilson FVM. Under the mesh assumption that the underlying mesh is an h2-parallelogram mesh, we show that the scheme possesses first order in the mesh-dependent H1-norm and second order in the L2-norm error estimates, the same optimal convergence orders as those of the corresponding Wilson finite element method (FEM). Numerical results are presented to demonstrate the theoretical results on the convergence order of the method.