Error analysis of stabilized semi-implicit method of Allen-Cahn
Xiaofeng Yang - Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States (email)
Abstract: We consider in this paper the stabilized semi-implicit (in time) scheme and the splitting scheme for the Allen-Cahn equation $\phi_t-\Delta\phi+$ε$^-2f(\phi)=0$ 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 ε-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.
Keywords: Allen-Cahn equation, semi-implicit methods, error
Received: July 2008; Revised: October 2008; Published: April 2009.
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