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Jung, Chang-Yeol
Numerical Analysis Lab.
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A staggered discontinuous Galerkin method for elliptic problems on rectangular grids

Author(s)
Kim, H. H.Jung, Chang-YeolNguyen, T. B.
Issued Date
2021-10
DOI
10.1016/j.camwa.2021.08.011
URI
https://scholarworks.unist.ac.kr/handle/201301/54617
Fulltext
https://www.sciencedirect.com/science/article/pii/S0898122121002959?via%3Dihub
Citation
COMPUTERS & MATHEMATICS WITH APPLICATIONS, v.99, pp.133 - 154
Abstract
In this article, a staggered discontinuous Galerkin (SDG) approximation on rectangular meshes for elliptic problems in two dimensions is constructed and analyzed. The optimal convergence results with respect to discrete. L-2 and H-1 norms are theoretically proved. Some numerical evidences to verify the optimal convergence rates are presented. Several numerical examples to the elliptic singularly perturbed problems with sharp boundary or interior layers are presented to show that the proposed SDG method is very effective, stable and accurate. Thanks to the simple structure of rectangular meshes, the discrete gradients across the boundaries of rectangular elements are easily defined, making numerical implementation much easier. The idea of using the rectangular meshes will be extended to more practical problems on a curved domain in future works.
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
ISSN
0898-1221
Keyword (Author)
Staggered discontinuous Galerkin methodsFinite volume methodsElliptic problemsRectangular meshesConvergence analysisBoundary and interior layers
Keyword
FINITE-VOLUME METHODDIFFUSION-EQUATIONSCONVERGENCESCHEME

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