A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations

A discontinuous Galerkin method with interior penalties is presented for nonlinear Sobolev equations. A semi-discrete and a family of Fully-discrete time approximate scheme are formulated. These schemes can be symmetric or nonsymmetric. Hp-version error estimates are analyzed for these schemes. Just because of a damping term del.(b(u)del u(t)) included in Sobolev equation, which is the distinct character different from parabolic equation, special test functions are chosen to deal with this term. Finally, a priori L(infinity)(H(1)) error estimate is derived for the semi-discrete time scheme and similarly, l(infinity)(H(1)) and l(2)(H(1)) for the Fully-discrete time schemes. These results also indicate that spatial rates in H1 and time truncation errors in L(2) are optimal. (C) 2007 Elsevier Inc. All rights reserved.