On the convergence rate of the cell discretization algorithm for solving elliptic problems

Abstract

Error estimates for the cell discretization algorithm are obtained for polynomial bases used to approximate both H k ( Ω ) {H^k}(\Omega ) and analytic solutions 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 approximations of the h-p method. The examples provided by our experiments provide discontinuous approximations that have errors similar to the finite element results.