A nonconforming covolume method for elliptic problems

We consider a control volume (covolume) method for second-order elliptic PDEs with the rotated-Q1 nonconforming finite element on rectangular grids. The coefficient κ may a variable, diagonal tensor, or discontinuous. We prove first-order convergence in H1 norm and second order convergence in L2 norm when the partition is square. Our numerical experiments show that our covolume scheme has about 30% less error than FEM even when κ is discontinuous tensor.