  We present and analyze three distinct semi-discrete schemes for solving
nonlocal geometric flows incorporating perimeter terms. These schemes are based
on the finite difference method, the finite element method, and the finite
element method with a specific tangential motion. We offer rigorous proofs of
quadratic convergence under $H^1$-norm for the first scheme and linear
convergence under $H^1$-norm for the latter two schemes. All error estimates
rely on the observation that the error of the nonlocal term can be controlled
by the error of the local term. Furthermore, we explore the relationship
between the convergence under $L^\infty$-norm and manifold distance. Extensive
numerical experiments are conducted to verify the convergence analysis, and
demonstrate the accuracy of our schemes under various norms for different types
of nonlocal flows.
