Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 198, Issue 21-26, Pages 1726-1741Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2009.01.021
Keywords
Finite element methods; Isogeometric analysis; k-Method; Approximation; n-Widths; Sup-inf
Funding
- Department of Energy [DE-FG02-97ER25308]
- Office of Naval Research [N00014-03-0263]
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We begin the mathematical study of the k-method utilizing the theory of Kolmogorov n-widths. The k-method is a finite element technique where spline basis functions of higher-order continuity are employed. It is a fundamental feature of the new field of isogeometric analysis. In previous works, it has been shown that using the k-method has many advantages over the classical finite element method in application areas such as structural dynamics, wave propagation, and turbulence. The Kolmogorov n-width and sup-inf were introduced as tools to assess the effectiveness of approximating functions. In this paper, we investigate the approximation properties of the k-method with these tools. Following a review of theoretical results, we conduct a numerical study in which we compute the n-width and sup-inf for a number of one-dimensional cases. This study sheds further light on the approximation properties of the k-method. We finish this paper with a comparison study of the k-method and the classical finite element method and an analysis of the robustness of polynomial approximation. (C) 2009 Elsevier B.V. All rights reserved.
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