Error Estimates for a Discontinuous Galerkin Method with Interior Penalties Applied to Nonlinear Sobolev Equations
نویسندگان
چکیده
A Discontinuous Galerkin method with interior penalties is presented for nonlinear Sobolev equations. A semi-discrete and a family of fully-discrete time approximate schemes are formulated. These schemes are symmetric. Hp-version error estimates are analyzed for these schemes. For the semi-discrete time scheme a priori L∞(H 1) error estimate is derived and similarly, l∞(H 1) and l2(H 1) for the fully-discrete time schemes. These results indicate that spatial rates in H 1 and time truncation errors in L2 are optimal. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 24: 879–896, 2008
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