# 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)
• 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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