A note on the rate of convergence of integration schemes for closed surfaces

被引：1
|
作者：
Zavalani, Gentian [1 ,2 ,3 ]
Shehu, Elima [4 ,5 ]
Hecht, Michael [1 ,2 ]
机构：
[1] Ctr Adv Syst Understanding CASUS, D-02826 Gorlitz, Germany
[2] Helmholtz Zentrum Dresden Rossendorf, D-01328 Dresden, Germany
[3] Tech Univ Dresden, Dresden, Germany
[4] Max Planck Inst Math Sci, Leipzig, Germany
[5] Osnabruck Univ, Osnabruck, Germany
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2024年 / 43卷 / 02期
关键词：
Numerical integration; Surface integrals; Convergence rates; Closest point projection; Chebyshev-Lobatto nodes;
D O I：
10.1007/s40314-024-02611-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we issue an error analysis for integration over discrete surfaces using the surface parametrization presented in Praetorius and Stenger (Arch Numer Softw 1(1):2022, 2022) as well as prove why even-degree polynomials utilized for approximating both the smooth surface and the integrand exhibit a higher convergence rate than odd-degree polynomials. Additionally, we provide some numerical examples that illustrate our findings and propose a potential approach that overcomes the problems associated with the original one.
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页数：17
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