Two-grid algorithm of lumped mass finite element approximation for Allen-Cahn equations

In this paper, we present a two-grid lumped mass finite element algorithm for 2D Allen-Cahn equations, where Crank-Nicolson scheme and piecewise linear element are utilized for temporal and spatial discretization, respectively. Both the maximum-norm boundedness and H1-norm error estimates of the proposed two-grid scheme are discussed. Finally, a numerical example is given to verify the theoretical results. By comparing with the finite element scheme and the two-grid finite element scheme, we found that our scheme has a great advantage in calculation time.