Construction of Cubature Formulas via Bivariate Quadratic Spline Spaces over Non-Uniform Type-2 Triangulation
Year: 2022
Author: Xiquan Shi, Jiang Qian, Jinming Wu, Dianxuan Gong
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 2 : pp. 205–230
Abstract
In this paper, matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in $S^1_2 (∆^{(2)}_{mn})$, and coefficients of splines in terms of B-net are reviewed firstly. Moreover, by means of coefficients in terms of B-net, computation of bivariate numerical cubature over triangular sub-domains with respect to variables $x$ and $y$ is transferred into summation of coefficients of splines in terms of B-net. Thus concise bivariate cubature formulas are constructed over rectangular sub-domain. Furthermore, by means of module of continuity and max-norms, error estimates for cubature formulas are derived over both sub-domains and the domain.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2008-m2020-0077
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 2 : pp. 205–230
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Multivariate spline Bivariate cubature Conformality of Smoothing Cofactor Method B-net Non-uniform Type-2 Triangulation.