The hybrid Wilson finite volume method for elliptic problems on quadrilateral meshes

摘要

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 h(2)-parallelogram mesh, we show that the scheme possesses first order in the mesh-dependent H-1-norm and second order in the L-2-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.