Ashort note on the error estimates of Yuan-Shu discontinuous Galerkin method based on non-polynomial approximation spaces
- 주제(키워드) Discontinuous Galerkin method , Non-polynomial approximation space , Wronskian , Extended Tchebycheff system , Approximation rate
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 ACADEMIC PRESS INC ELSEVIER SCIENCE
- 발행년도 2016
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000130513
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jcp.2016.05.032
초록/요약
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.
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