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 ∇·(b(u)∇ut) 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∞(H1) error estimate is derived for the semi-discrete time scheme and similarly, l∞(H1) and l2(H1) for the Fully-discrete time schemes. These results also indicate that spatial rates in H1 and time truncation errors in L2 are optimal.