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Bull. Korean Math. Soc. 2011; 48(5): 897-915

Printed September 1, 2011

https://doi.org/10.4134/BKMS.2011.48.5.897

Copyright © The Korean Mathematical Society.

$L^2$-error analysis of fully discrete discontinuous Galerkin approximations for nonlinear Sobolev equations

Mi Ray Ohm and Hyun Young Lee

Dongseo University, Kyungsung University

Abstract

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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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