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 $L^2$-error analysis of fully discrete discontinuous Galerkin approximations for nonlinear Sobolev equations Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 897-915 https://doi.org/10.4134/BKMS.2011.48.5.897Printed September 1, 2011 Mi Ray Ohm and Hyun Young Lee Dongseo University, Kyungsung University Abstract : In this paper, we develop a symmetric Galerkin method with interior penalty terms to construct fully discrete approximations of the solution for nonlinear Sobolev equations. To analyze the convergence of discontinuous Galerkin approximations, we introduce an appropriate projection and derive the optimal $L^2$ error estimates. Keywords : nonlinear Sobolev equation, discontinuous Galerkin approximation, fully discrete approximations, optimal $L^2$ error estimates MSC numbers : 65M15, 65N30 Downloads: Full-text PDF