Journal of the Korean Society for Industrial and Applied Mathematics

  • 제20권4호
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  • Pages.295-308
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  • 2016
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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SUPERCONVERGENCE OF HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC EQUATIONS

  • MOON, MINAM (DEPARTMENT OF MATHEMATICS, KOREA MILITARY ACADEMY) ;
  • LIM, YANG HWAN (DEPARTMENT OF MATHEMATICS, KOREA MILITARY ACADEMY)
  • 투고 : 2016.09.26
  • 심사 : 2016.11.24
  • 발행 : 2016.12.25
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초록

We propose a projection-based analysis of a new hybridizable discontinuous Gale-rkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses $L^2$-projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p + 1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.

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과제정보

연구 과제 주관 기관 : Hwa-Rang Dae Research Institute

참고문헌

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