@Article{JCM-40-205,
author = {Shi , XiquanQian , JiangWu , 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 = {http://global-sci.org/intro/article_detail/jcm/20184.html}
}