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Ashort note on the error estimates of Yuan-Shu discontinuous Galerkin method based on non-polynomial approximation spaces

Title
Ashort note on the error estimates of Yuan-Shu discontinuous Galerkin method based on non-polynomial approximation spaces
Authors
Yang, HyoseonYoon, Jungho
Ewha Authors
윤정호
SCOPUS Author ID
윤정호scopus
Issue Date
2016
Journal Title
JOURNAL OF COMPUTATIONAL PHYSICS
ISSN
0021-9991JCR Link1090-2716JCR Link
Citation
vol. 320, pp. 33 - 39
Keywords
Discontinuous Galerkin methodNon-polynomial approximation spaceWronskianExtended Tchebycheff systemApproximation rate
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
In the article [Yuan and Shu (2006) [17]], Yuan and Shu have developed discontinuous Galerkin ( DG) methods based on non-polynomial approximation spaces for solving time dependent problems. The authors established L-2 error estimates of the proposed methods and also presented a criterion for the choice of basis functions of the non-polynomial spaces to have the same approximation rates as those of polynomial finite element spaces of the same dimension. However, the verification that some of approximation spaces do satisfy the criterion has been performed only to limited types of approximation spaces. In this regards, the aim of this short note is to fill the gap. We prove that the criterion of Yuan and Shu can be satisfied by a wide class of basis functions, including the well-known basis functions such as trigonometric and exponential polynomials. (C) 2016 Elsevier Inc. All rights reserved.
DOI
10.1016/j.jcp.2016.05.032
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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