Efficient Linearly and Unconditionally Energy Stable Schemes for the Phase Field Model of Solid-State Dewetting Problems

In this paper, we study linearly first and second order in time, uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel approach SAV (scalar auxiliary variable), a new developed efficient and accurate method for a large class of gradient flows. The schemes are based on the first order Euler method and the second order backward differential formulas(BDF2) for time discretization, and finite element methods for space discretization. It is shown that the schemes are unconditionally stable and the discrete equations are uniquely solvable for all time steps. We present some numerical experiments to validate the stability and accuracy of the proposed schemes.