Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (2): 385-394.

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A New Absolutely Stable hp Discontinuous Galerkin Methodfor the Reaction-Diffusion Problem

Ge Zhihao1, Cao Jiwei2   

  1. 1. Institute of Applied Mathematics & School of Mathematics and Statistics, Henan University, Henan Kaifeng 475004;
    2. College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450000
  • Received:2016-12-22 Revised:2017-09-01 Online:2018-04-26 Published:2018-04-26
  • Supported by:
    Supported by the Natural Science Foundation of Henan Province (162300410031), and the Excellent Youth Program of the Basic Research Operating Expenses Program of Henan Province (yqpy20140039)

Abstract: In this paper, a new absolutely stable hp discontinuous Galerkin method is proposed. And the error estimate of hp discontinuous Galerkin method is given, and the optimal convergent orders in L2-norm and H1-norm for the general stabilization parameters are proved. Finally, the numerical tests verify the theoretical results.

Key words: Reaction-diffusion problem, Discontinuous Galerkin method, Optimal error estimation

CLC Number: 

  • O241.82
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