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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. China

    Fuzheng Gao, Jianxian Qiu & Qiang Zhang

  2. School of Mathematics, Shandong University, Jinan, 250100, P.R. China

    Fuzheng Gao

Authors
  1. Fuzheng Gao
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  2. Jianxian Qiu
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  3. Qiang Zhang
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Corresponding author

Correspondence to Qiang Zhang.

Additional information

The research was partially supported by Jiangsu Province Postdoctoral Science Foundation, and NSFC (grant no. 10671091 and 10871093).

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Gao, F., Qiu, J. & Zhang, Q. Local Discontinuous Galerkin Finite Element Method and Error Estimates for One Class of Sobolev Equation. J Sci Comput 41, 436–460 (2009). https://doi.org/10.1007/s10915-009-9308-y

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  • DOI: https://doi.org/10.1007/s10915-009-9308-y

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