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Type: Journal article
Title: DIV-CURL vector quasi-interpolation on a finite domain
Author: Chen, F.
Suter, D.
Citation: Mathematical and Computer Modelling, 1999; 30(1-2):179-204
Publisher: Elsevier
Issue Date: 1999
ISSN: 0895-7177
Statement of
F. Chen and D. Suter
Abstract: This paper presents a quasi-interpolation method for DIV-CURL vector splines in two dimensions on both infinite and finite domains. The quasi-interpolant is a linear combination of translates of dilates of a basis function. In particular, our discussion focuses on the approximation of a vector-valued function defined on a finite domain for practical application purposes. In such a case, edge functions are introduced for preserving the convergence of the quasi-interpolant on the boundaries. These edge functions can be determined by means of the polynomial reproduction properties of the quasi-interpolation. The analysis of convergence has shown that the quasi-interpolant defined on a regular grid of whole R2 can reproduce linear polynomial and has an O(h2 | log h|) error bound, while the modified quasi-interpolant defined on a square I2 has an O(h) error bound if the edge functions are designed for reproducing a constant.
Keywords: Quasi-interpolation; Polynomial reproduction; DIV-CURL vector splines; Edge functions
Rights: ©1999 Elsevier Science Ltd.
DOI: 10.1016/S0895-7177(99)00124-7
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