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DISCONTINUOUS GALERKIN SPECTRAL ELEMENT METHOD FOR ELLIPTIC PROBLEMS BASED ON FIRST-ORDER HYPERBOLIC SYSTEM

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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 ??(????+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.
Author(s)
김덕훈안형택
Issued Date
2021
Type
Article
Keyword
Discontinuous Galerkin(DG) methodSpectral element methodPoisson equationFirst order hyperbolic system(FOHS).
DOI
10.12941/jksiam.2021.25.173
URI
https://oak.ulsan.ac.kr/handle/2021.oak/8838
https://ulsan-primo.hosted.exlibrisgroup.com/primo-explore/fulldisplay?docid=TN_cdi_nrf_kci_oai_kci_go_kr_ARTI_9900933&context=PC&vid=ULSAN&lang=ko_KR&search_scope=default_scope&adaptor=primo_central_multiple_fe&tab=default_tab&query=any,contains,DISCONTINUOUS%20GALERKIN%20SPECTRAL%20ELEMENT%20METHOD%20FOR%20ELLIPTIC%20PROBLEMS%20BASED%20ON%20FIRST-ORDER%20HYPERBOLIC%20SYSTEM&offset=0&pcAvailability=true
Publisher
Journal of the Korean Society for Industrial and Applied Mathematics
Location
대한민국
Language
영어
ISSN
1226-9433
Citation Volume
25
Citation Number
4
Citation Start Page
173
Citation End Page
195
Appears in Collections:
Engineering > Aerospace Engineering
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