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A low order characteristic-nonconforming finite element method for nonlinear Sobolev equation with convection-dominated term

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  • Shi, Dongyang
  • Tang, Qili
  • Gong, Wei

Abstract

A low order nonconforming finite element method is combined with the method of characteristics to treat the nonlinear Sobolev equation with convection-dominated term. The optimal order error estimates in a broken H1-norm and L2-norm are obtained by some special properties of the interpolation operator and the mean value trick, instead of the so-called elliptic projection which is an indispensable tool in the convergence analysis of the previous literature. In addition, the global superconvergence is derived based on the interpolated postprocessing technique. The theoretical results are confirmed by some numerical experiments.

Suggested Citation

  • Shi, Dongyang & Tang, Qili & Gong, Wei, 2015. "A low order characteristic-nonconforming finite element method for nonlinear Sobolev equation with convection-dominated term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 114(C), pages 25-36.
    • Handle: RePEc:eee:matcom:v:114:y:2015:i:c:p:25-36
    DOI: 10.1016/j.matcom.2014.03.008
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    References listed on IDEAS

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    1. Zhou, Zhaojie & Chen, Fengxin & Chen, Huanzhen, 2012. "Characteristic mixed finite element approximation of transient convection diffusion optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2109-2128.
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    Cited by:

    1. Shi, Dongyang & Wang, Junjun, 2017. "Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite element," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 1-16.
    2. Shi, Dongyang & Wang, Junjun, 2017. "Unconditional superconvergence analysis of conforming finite element for nonlinear parabolic equation," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 216-226.
    3. Li, Xiaoli & Rui, Hongxing, 2019. "A block-centered finite difference method for the nonlinear Sobolev equation on nonuniform rectangular grids," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.

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