In this paper, the proposed method utilizes finite difference and Fourier series methods to calculate the mean curvature vectors and normalized curvature weights at the vertices of manifold triangular meshes. Specifically, this stable method achieves the $L^2$ convergence of the mean curvature vector. Furthermore, by comparing the method proposed in this paper with previously proposed classical methods, the results show that this method effectively balances precision and stability, and significantly reduces the larger errors observed on triangular meshes with small angles (approximately $0^◦$ ).