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Error analysis of stabilized semi-implicit method of Allen-Cahn equation

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  • 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.
    Mathematics Subject Classification: Primary: 65M12, 76T99; Secondary: 65M70.

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