A priori error estimate for the Baumann-Oden version of the discontinuous Galerkin method

This work presents an a priori error estimate for hp finite element approxi mations obtained by the Baumann-Oden version of the Discontinuous Galerkin method. If it is now well known that the method converges with an optimal r ate in h, this has not been yet proved or disproved with respect to p. For the Poisson problem and for solutions with regularity s, it is shown here t hat the rate of convergence can be reduced to p(s-5/2). It is also suggeste d that this rate could still be improved. (C) 2001 Academie des sciences/Ed itions scientifiques et medicales Elsevier SAS.