Error analysis of stabilized semi-implicit method of Allen-Cahnequation

We consider in this paper the stabilized semi-implicit (intime) scheme and the splitting scheme for the Allen-Cahn equationφₜ-Δφ+ε⁻2f(φ)=0 arising from phasetransitions in material science. For the stabilizedfirst-order scheme, we show that it is unconditionally stable andthe error bound depends on ε-1 in some lower polynomialorder using the spectrum estimate of [2, 10, 11]. In addition, the first- andsecond-order operator splitting schemes are proposed and theaccuracy are tested and compared with the semi-implicit schemesnumerically.