Semi-Implicit Methods for Phase Field Equations
A/Prof. Zhong-Hua Qiao
Department of Applied Mathematics, The Hong Kong Polytechnic University

Recent results in the literature provide computational evidence that the stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth order nonlinear diffusion. The up-to-date theoretical explanation of the numerical stability relies on the assumption that the derivative of the nonlinear potential function satisfies a Lipschitz-type condition, which in a rigorous sense, implies the boundedness of the numerical solution. In this work, we remove the Lipschitz assumption on the nonlinearity and prove unconditional energy stability for the stabilized semi-implicit time-stepping methods. It is shown that the size of the stabilization term depends on the initial energy and the perturbation parameter but is independent of the time step.

About the Speaker


2019-12-02 2:30 PM
Room: A203 Meeting Room
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