题目：Efficient, accurate and energy stable discontinuous Galerkin methods for phase field models
报告人：徐岩（中国科技大学 数学科学学院）
时间：2021/01/18（周一）10:00-11:30（北京时间）
地点：腾讯会议
会议号：531 596 920
摘要：The goal of this paper is to propose fully discrete discontinuous Galerkin (DG) finite element methods for the phase field models, which are shown to be unconditionally energy stable. In details, using the convex splitting principle, we first construct a first order scheme and a second order Crank-Nicolson scheme for time discretizations. The proposed schemes are shown to be unconditionally energy stable. Then, using the invariant energy quadratization approach, we develop a novel linear and decoupled first and second order scheme, which is easy to implement and energy stable. In addition, a semi-implicit spectral deferred correction method combining with low scheme is employed to improve the temporal accuracy. Due to the local properties of the DG methods, the resulting algebraic equations at the implicit level is easy to implement and can be solved in an explicit way when it is coupled with iterative methods. In particular, we present efficient and practical multigrid solvers to solve the resulting algebraic equations, which have nearly optimal complexity. Numerical experiments of the accuracy and long time simulations are presented to illustrate the high order accuracy in both time and space, the capability and efficiency of the proposed methods.
报告人简介：徐岩，中国科技大学数学科学学院教授, 博士生导师。2008年全国优秀博士论文；2009年新世纪大学优秀人才；2017年荣获国家优秀青年科学基金；担任Communication on Applied Mathematics and Computation以及Advances in Applied Mathematics and Mechanics的编委；2019年至今担任Journal of Scientific Computing的编委；主要研究针对非线性波动方程、MHD方程、不可压NS方程、双线性泊松Brackets方程的ENO、WENO、DG、LDG方法。发表学术论文80余篇，其中主要发表在Nature Science、JCM、JCP、Communications in Computational Physics、SIAM Journal on Scientific Computing等
