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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)
  • Received : 2016.09.26
  • Accepted : 2016.11.24
  • Published : 2016.12.25

Abstract

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.

Acknowledgement

Supported by : Hwa-Rang Dae Research Institute

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