Back to Search
Start Over
n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method
- Source :
-
Computer Methods in Applied Mechanics & Engineering . May2009, Vol. 198 Issue 21-26, p1726-1741. 16p. - Publication Year :
- 2009
-
Abstract
- Abstract: 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00457825
- Volume :
- 198
- Issue :
- 21-26
- Database :
- Academic Search Index
- Journal :
- Computer Methods in Applied Mechanics & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 37346933
- Full Text :
- https://doi.org/10.1016/j.cma.2009.01.021