Error estimates using the cell discretization method for steady-state convection-diffusion equations

The cell discretization algorithm is applied to generate approximate solutions for some second-order non-self-adjoint elliptic equations. General convergence for homogeneous problems is shown by obtaining suitable error estimates. The method is applied using polynomial bases; this provides a nonconforming extension of the finite element method that can also produce the continuous approximations of an h-p finite element method. Numerical tests on convection-diffusion problems are made that confirm the theoretical estimates, and methods for dealing with boundary layer problems are illustrated.