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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Cheng Wang, Department of Mathematics, University of Massachusetts Dartmouth

Inviter: 谢和虎
Title:
Energy stable fourth order finite difference scheme for the Cahn-Hilliard equation
Time & Venue:
2018.8.10 10:00-11:00 Z311
Abstract:

An energy stable numerical scheme for the Cahn-Hilliard equation is proposed and analyzed, with second order accuracy in time and the fourth order finite difference approximation in space. In particular, the truncation error for the long stencil fourth order finite difference approximation is estimated, over a uniform numerical grid with a periodic boundary condition,via the help of discrete Fourier analysis instead of the the standard Taylor expansion. This in turn results in a reduced regularity requirement for the test function. In the temporal approximation, we apply a second order BDF stencil, combined with a second order extrapolation formula applied to the concave diffusion term, as well as a second order artificial Douglas-Dupont regularization term, for the sake of energy stability. As a result, the unique solvability, energy stability are established for the proposed numerical scheme, and an optimal rate convergence analysis is derived. A few numerical experiments are also presented.

 

 

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