Stability of Semi-implicit Methods in Phase Field Models

Prof. Dong LI (dli@math.ubc.ca)

Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T1Z2, Canada

Abstract: Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear diffusion, with typical examples like the Cahn-Hilliard equation and the thin film type equation. 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. I will discuss a group of recent results which remove the Lipschitz assumption on the nonlinearity and prove unconditional energy stability for the stabilized semi-implicit time-stepping methods. Time permitting I will also mention some more recent developments.

Time： 2017-07-18 14：00-15：00

Address: Room 316, The environment building of Renmin University of China