Local Discontinuous Galerkin Finite Element Method and Error Estimates for One Class of Sobolev Equation

Authors:
Fuzheng Gao;Jianxian Qiu;Qiang Zhang
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093 and School of Mathematics, Shandong University, Jinan, P.R. China 250100;Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093;Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093
Venue:
Journal of Scientific Computing
Year:
2009

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Abstract

In this paper we present a numerical scheme based on the local discontinuous Galerkin (LDG) finite element method for one class of Sobolev equations, for example, generalized equal width Burgers equation. The proposed scheme will be proved to have good numerical stability and high order accuracy for arbitrary nonlinear convection flux, when time variable is continuous. Also an optimal error estimate is obtained for the fully discrete scheme, when time is discreted by the second order explicit total variation diminishing (TVD) Runge-Kutta time-marching. Finally some numerical results are given to verify our analysis for the scheme.