@Article{JCM-40-2,
author = {Xiquan, Shi and Qian, Jiang and Wu, Jinming and Gong, Dianxuan},
title = {Construction of Cubature Formulas via Bivariate Quadratic Spline Spaces over Non-Uniform Type-2 Triangulation},
journal = {Journal of Computational Mathematics},
year = {2022},
volume = {40},
number = {2},
pages = {205--230},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2008-m2020-0077},
url = {https://global-sci.com/article/84175/construction-of-cubature-formulas-via-bivariate-quadratic-spline-spaces-over-non-uniform-type-2-triangulation}
}