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.