报告题目：The second-order accurate convex splitting scheme for the Cahn-Hilliard equation:

Crank-Nicholson and BDF approaches

报告人：Cheng Wang，University of South Carolina

时  间：2015年7月20日    下午4:00―5:00

地  点：东区管理科研楼  数学科学学院1218室

内容提要：

The second order accurate schemes are presented for the 2-D and 3-D Cahn-Hilliard equation, and an error analysis with an improved convergence constant is provided. Both the modified Crank-Nicholson and the backward differentiation formula (BDF) versions will be discussed. The unique solvability and unconditional energy stability results from its convex splitting nature. Meanwhile, it is observed that a standard error estimate gives a convergence constant which depends on certain interface parameter in an exponentially grown singular grown form. To overcome this well-known difficulty, we apply a spectrum estimate for the linearized Cahn-Hilliard operator and get an improved estimate, in which the convergence constant depends on the physical parameter only in a polynomial order, other than the exponential growth one.