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.

引用

页数：17

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