Construction of Cubature Formulas via Bivariate Quadratic Spline Spaces over Non-Uniform Type-2 Triangulation

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.

Author Details

Xiquan Shi

Jiang Qian

Jinming Wu

Dianxuan Gong

  1. On spline quasi-interpolation through dimensions

    Dagnino, Catterina

    Lamberti, Paola

    Remogna, Sara

    ANNALI DELL'UNIVERSITA' DI FERRARA, Vol. 68 (2022), Iss. 2 P.397

    https://doi.org/10.1007/s11565-022-00427-4 [Citations: 5]