Let $\mathbb{S}^{2}$ be the unit sphere, $\Delta_{s}$ the Laplace-Beltrami operator, $U_h$ the finite element space in $\mathbb{S}^{2}$ and $V_{h}$ the space of constant function associated to $U_{h}$. Let me consider ${\bf S}_{h}$ as the piecewise polygonal approximation of $\mathbb{S}^{2}$. I need to change the variables of $\mathbb{S}^{2}$ to ${\bf S}_{h}$. In particular, how to use the change of variables formula for
$$\int_{\widetilde{T}}\Delta_{s}u_{h}(x)[v_{h}(x)-I_{h}(v_{h})(x)]ds(x),\quad \text{for each }u_{h},v_{h}\in U_{h}$$ where $\widetilde{T}$ is a spherical triangle, and $I_{h}$ is the interpolant operator of $U_{h}$ on $V_{h}$.