Journal of the Korean Society for Industrial and Applied Mathematics

  • 제26권4호
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  • Pages.244-262
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  • 2022
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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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HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD FOR ELLIPTIC EQUATIONS WITH NONLINEAR COEFFICIENTS

  • MINAM, MOON (DEPARTMENT OF MATHEMATICS, KOREA MILITARY ACADEMY)
  • 투고 : 2022.07.12
  • 심사 : 2022.12.12
  • 발행 : 2022.12.25
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초록

In this paper, we analyze the hybridizable discontinuous Galerkin (HDG) method for second-order elliptic equations with nonlinear coefficients, which are used in many fields. We present the HDG method that uses a mixed formulation based on numerical trace and flux. Under assumptions on the nonlinear coefficient and H2-regularity for a dual problem, we prove that the discrete systems are well-posed and the numerical solutions have the optimal order of convergence as a mesh parameter. Also, we provide a matrix formulation that can be calculated using an iterative technique for numerical experiments. Finally, we present representative numerical examples in 2D to verify the validity of the proof of Theorem 3.10.

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과제정보

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2020R1F1A1A01072414, NRF-2022R1F1A1069217).

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