A note on the rate of convergence of integration schemes for closed surfaces
Gentian Zavalani, Elima Shehu, Michael Hecht · Computational and Applied Mathematics · 2024
Abstract 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.