Convergence of isoparametric BGN methods for mean curvature flow of closed surfaces with high-order finite elements

We prove the convergence of the isoparametric Barrett--Garcke--Nürnberg (BGN) method for mean curvature flow of closed surfaces. For finite elements of degree $k\ge6$ and time steps $τ=O(h^2)$, the numerical surfaces converge to the exact surfaces in the manifold distance with order $h^2$. The proof