In this talk, I will present a framework for devising unconditionally stable schemes for general dissipative systems based on a generalized positive auxiliary variable (gPAV). This method requires the solution of a linear equation to be solved for each time step only once, so the computational cost is almost the same with the classical semi-implicit method. Rigorous error estimate and applications of this method to multiphase flow problems are also presented. 

杨志国博士毕业于新加坡南洋理工大学，后前往普渡大学任访问助理教授，现任上海交通大学数学科学学院副教授。他致力于流体、电磁高精度算法的研究工作，在计算数学的高水平期刊如SIAM系列、JCP、CMAME上发表多篇论文。