ERROR ANALYSIS OF STABILIZED SEMI-IMPLICIT METHOD OF ALLEN-CAHN EQUATION

We consider in this paper the stabilized semi-implicit (in time) scheme and the splitting scheme for the Allen-Cahn equation phi(t) - Delta phi + epsilon(-2) f (phi) = 0 arising from phase transitions in material science. For the stabilized first-order scheme, we show that it is unconditionally stable and the error bound depends on epsilon(-1) in some lower polynomial order using the spectrum estimate of [2, 10, 11]. In addition, the first- and second-order operator splitting schemes are proposed and the accuracy are tested and compared with the semi-implicit schemes numerically.