Title: Numerical methods for some phase field models and their approximations to geometric flows
Speaker: Yukun Li (Ohio State University)
Abstract: In this talk, I will briefly talk about the backgrounds about phase field models, level set models and geometric flows. Then I will state all the relations between these phase field models and their corresponding geometric flows. Besides, the accuracy and efficiency of different numerical schemes will be theoretically and numerically compared, and a scheme which satisfies the discrete maximum principle will be firstly designed. Furthermore, we will discuss the (discrete) spectrum estimates, which play important roles in analyzing the asymptotic behaviors of the (numerical) solutions of the phase field models. To prove the relations between our numerical solutions and the geometric flows, different bridges between the conforming and nonconforming elements will be constructed. Finally, some numerical tests are given to verify the evolutions of the solutions, which are consistent with the corresponding geometric laws.
