TY - JOUR
T1 - Construction of Cubature Formulas via Bivariate Quadratic Spline Spaces over Non-Uniform Type-2 Triangulation
AU - Shi , Xiquan
AU - Qian , Jiang
AU - Wu , Jinming
AU - Gong , Dianxuan
JO - Journal of Computational Mathematics
VL - 2
SP - 205
EP - 230
PY - 2022
DA - 2022/01
SN - 40
DO - http://doi.org/10.4208/jcm.2008-m2020-0077
UR - https://global-sci.org/intro/article_detail/jcm/20184.html
KW - Multivariate spline, Bivariate cubature, Conformality of Smoothing Cofactor Method, B-net, Non-uniform Type-2 Triangulation.
AB - <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>