$L^2$-error analysis of fully discrete discontinuous Galerkin approximations for nonlinear Sobolev equations
Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 897-915
Printed 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
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