ON THE CONVERGENCE RATE OF THE CELL DISCRETIZATION ALGORITHM FOR SOLVING ELLIPTIC PROBLEMS

Error estimates for the cell discretization algorithm are obtained for polynomial bases used to approximate both H-k(Omega) and analytic sol utions to selfadjoint elliptic problems. The polynomial implementation of this algorithm can be viewed as a nonconforming version of the h-p finite element method that also can produce the continuous approximat ions of the h-p method. The examples provided by our experiments provi de discontinuous approximations that have errors similar to the finite element results.