Hybrid Spectral Difference Methods for an Elliptic Equation

Youngmok Jeon; Eun Jae Park; Dong Wook Shin

doi:10.1515/cmam-2016-0043

Hybrid Spectral Difference Methods for an Elliptic Equation

Youngmok Jeon, Eun Jae Park, Dong Wook Shin

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

A locally conservative, hybrid spectral difference method (HSD) is presented and analyzed for the Poisson equation. The HSD is composed of two types of finite difference approximations; the cell finite difference and the interface finite difference. Embedded static condensation on cell interior unknowns considerably reduces the global couplings, resulting in the system of equations in the cell interface unknowns only. A complete ellipticity analysis is provided. The optimal order of convergence in the semi-discrete energy norms is proved. Several numerical results are given to show the performance of the method, which confirm our theoretical findings.

Original language	English
Pages (from-to)	253-267
Number of pages	15
Journal	Computational Methods in Applied Mathematics
Volume	17
Issue number	2
DOIs	https://doi.org/10.1515/cmam-2016-0043
Publication status	Published - 2017 Apr 1

Bibliographical note

Funding Information:
Y. Jeon was supported by National Research Foundation of Korea (NRF-2015R1D1A1A09057935). E.-J. Park was supported by National Research Foundation of Korea (NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358).

Publisher Copyright:
© 2017 by De Gruyter.

All Science Journal Classification (ASJC) codes

Numerical Analysis
Computational Mathematics
Applied Mathematics

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Cite this

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abstract = "A locally conservative, hybrid spectral difference method (HSD) is presented and analyzed for the Poisson equation. The HSD is composed of two types of finite difference approximations; the cell finite difference and the interface finite difference. Embedded static condensation on cell interior unknowns considerably reduces the global couplings, resulting in the system of equations in the cell interface unknowns only. A complete ellipticity analysis is provided. The optimal order of convergence in the semi-discrete energy norms is proved. Several numerical results are given to show the performance of the method, which confirm our theoretical findings.",

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AB - A locally conservative, hybrid spectral difference method (HSD) is presented and analyzed for the Poisson equation. The HSD is composed of two types of finite difference approximations; the cell finite difference and the interface finite difference. Embedded static condensation on cell interior unknowns considerably reduces the global couplings, resulting in the system of equations in the cell interface unknowns only. A complete ellipticity analysis is provided. The optimal order of convergence in the semi-discrete energy norms is proved. Several numerical results are given to show the performance of the method, which confirm our theoretical findings.

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Hybrid Spectral Difference Methods for an Elliptic Equation

Abstract

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