Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential

讲座标题:Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential

主讲人: 王成 副教授

讲座时间:1月18号(周四)下午10:00-12:00

讲座语言:中文,英文

主办单位:数学学院


讲座内容:

The Cahn-Hilliard model with logarithmic potential is considered, in which the key difficulty has always been associated with the singularity of the logarithmic terms. An energy stable finite difference scheme, which implicitly treats the logarithmic terms, is proposed and analyzed in this talk. In particular, how to ensure the positivity of the logarithmic arguments, so that the numerical scheme is well-defined at a point-wise level, has been a long-standing mathematical challenge. It is proved that, given any numerical solution with a fixed bound at the previous time step, there exists a unique numerical solution that satisfies the given bound (-1,1) at a point-wise level. As a result, the numerical scheme is proven to be well-defined, and the unique solvability and energy stability could be established with the help of convexity analysis. In addition, an optimal rate convergence analysis could be appropriately established. Some numerical results are also presented in the talk.


主讲人简介:

王成 副教授 University of Massachusetts Dartmouth