Efficient Linear Schemes with Unconditional Energy Stability for the Phase Field Model of Solid-State Dewetting Problems (Journal of Computational Mathematics, 2020)
In this paper, we study linearly first and second order in time, uniquely solvable andunconditionally energy stable numerical schemes to approximate the phase field modelof solid-state dewetting problems based on the novel "scalar auxiliary variable" (SAV)approach, 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 backwarddifferential formulas (BDF2) for time discretization, and finite element methods for spacediscretization. The proposed schemes are proved to be unconditionally stable and thediscrete equations are uniquely solvable for all time steps. Various numerical experimentsare presented to validate the stability and accuracy of the proposed schemes.
Keywords: Phase field models; Solid-state dewetting; SAV; Energy stability; Surface diffusion; Finite element method.