In this paper, we issue an error analysis for integration over discrete surfaces using the surface parametrization presented in [PS22] as well as prove why even-degree polynomials 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.

翻译：本文利用[PS22]中提出的曲面参数化方法，对离散曲面上的积分进行了误差分析，并证明了为何偶次多项式比奇次多项式具有更高的收敛速度。此外，我们通过数值算例直观展示了上述结论，并提出了一种能够克服原始方法中存在的问题的潜在改进方案。