Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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DISCONTINUOUS GALERKIN SPECTRAL ELEMENT METHOD FOR ELLIPTIC PROBLEMS BASED ON FIRST-ORDER HYPERBOLIC SYSTEM

  • KIM, DEOKHUN (SCHOOL OF NAVAL ARCHITECTURE AND OCEAN ENGINEERING, UNIVERSITY OF ULSAN) ;
  • AHN, HYUNG TAEK (SCHOOL OF NAVAL ARCHITECTURE AND OCEAN ENGINEERING, UNIVERSITY OF ULSAN)
  • Received : 2021.09.07
  • Accepted : 2021.11.12
  • Published : 2021.12.25
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Abstract

A new implicit discontinuous Galerkin spectral element method (DGSEM) based on the first order hyperbolic system(FOHS) is presented for solving elliptic type partial different equations, such as the Poisson problems. By utilizing the idea of hyperbolic formulation of Nishikawa[1], the original Poisson equation was reformulated in the first-order hyperbolic system. Such hyperbolic system is solved implicitly by the collocation type DGSEM. The steady state solution in pseudo-time, which is the solution of the original Poisson problem, was obtained by the implicit solution of the global linear system. The optimal polynomial orders of 𝒪(𝒽𝑝+1)) are obtained for both the solution and gradient variables from the test cases in 1D and 2D regular grids. Spectral accuracy of the solution and gradient variables are confirmed from all test cases of using the uniform grids in 2D.

Keywords

Acknowledgement

This work was supported by the National Supercomputing Center with supercomputing resources including technical support (KSC-2020-CRE-0119).

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