Variable Step BDF2 and Its Application to Cahn-Hilliard Equation
讲座名称：
Variable Step BDF2 and Its Application to Cahn-Hilliard Equation
讲座时间：
2019-12-07
讲座人：
王晓明
形式：
校区：
兴庆校区
实践学分：
讲座内容：
报告题目: Variable Step BDF2 and Its Application to Cahn-Hilliard Equation
报告时间：2019年12月7日，星期六，上午10:00-12:00
报告地点：数学与统计学院 数学楼2-1室
报告人： 王晓明教授，南方科技大学
报告摘要:
We propose and analyze a variable step second-order backward difference formula (BDF2) based scheme for the Cahn-Hilliard equation that is long-time energy stable and uniquely solvable. Such a variable step approach is an essential ingredient in improving the performance of numerical schemes. However, the rigorous analysis of variable step BDF2 scheme is a challenge. Current second-order error analysis contains a prefactor that could blow up at vanishing step size even in the linear parabolic case. The construction of our new scheme consists of three ideas: variable step BDF2, convex splitting, and viscous regularization. We establish the second-order convergence of our scheme with the aid of a novel discrete Gronwall type inequality without severe restriction on the ratio of successive time steps. Such a result is significant, even in the linear case. Numerical results corroborating our theoretical findings will be reported as well.
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