管理员登录 / English
A Time Splitting Space Spectral Element Method for the Cahn-Hilliard Equation
发布时间: 2017-12-03     13:03   【返回上一页】 发布人:陈丽贞


北京师范大学数学科学学院

 

周五公众报告

 

 

报告题目: A Time Splitting Space Spectral Element Method for the Cahn-Hilliard        
Equation

报告人:陈丽贞 (北京计算科学研究中心)

时间地点:128日,1500—1600 后主楼1124

报告摘要:
We propose and analyse a class of fully discrete schemes for the Cahn-Hilliard equation with Neumann boundary conditions. The schemes combine large-time step splitting methods in time and spectral element methods in space. We are particularly interested in analysing a class of methods that split the original Cahn-Hilliard equation into lower order equations. These lower order equations are simpler and less computationally expensive to treat. For the first-order splitting scheme, the stability and convergence properties are investigated based on an energy method. It is proven that both semi-discrete and fully discrete solutions satisfy the energy dissipation and mass conservation properties hidden in the associated continuous problem. A rigorous error estimate, together with numerical confirmation, is provided. Although not yet rigorously proven, higher-order schemes are also constructed and tested by a series of numerical examples. Finally, the proposed schemes are applied to the phase field simulation in a complex domain, and some interesting simulation results are obtained.

 

 

周五学院公众报告主旨:讲解现代数学中的基本概念、重要结果及其数学思想的起源、方法的创新等,扩展我们的教师和研究生的视野、提高数学修养以及增强学院的学术氛围。邀请各方向的专家用通俗易懂的报告内容、自由互动的讲解方式展现现代数学中重要的基本概念和深刻原理,让听众可以领略到现代数学理论其实是来源于一些大学或研究生阶段就熟知的古典数学中的想法和结论。希望这些报告有助于高年级的本科生、研究生和教师更全面的认识现代数学、享受数学之美。欢迎大家踊跃参与!