题目：A layers capturing type H-adaptive FEM for convection-diffusion-reaction equations on surfaces
报告人：冯新龙（新疆大学数学与系统科学学院）
时间：2020/10/29（周四）14:30-15:30
地点：数学学院425会议室
摘要：In this work, we study the FE approximation of surface convection-diffusion-reaction equations which are important fundamental model problems in simulations of complex physical phenomena on moving interfaces, ultra-thin materials and biological films. The optimal error estimates of FEM are shown. According to the analyze results, the solutions of convection-dominated diffusion problems have low accuracy in the regions of layers. To overcome such drawback which may lead to non-physical oscillations, the adaptive mesh refinement method is considered. Due to the numerical characteristic of non-physical oscillations and layers, we present an error estimator which specializes in capturing the non-physical oscillations and layers. The mesh refinement marking strategies which take into account the large curvatures of the surfaces are developed. The proposed method can efficiently capture layers, non-physical oscillations and provide high resolution solutions with fewer degree of freedoms. A series of numerical examples are designed to demonstrate the effectiveness of the proposed H-adaptive method and make exploration of the solution behavior of convection-dominated diffusion problems on surfaces.
报告人简介：冯新龙，现为新疆大学数学与系统科学学院教授, 博士生导师。主要研究科学计算、不确定性量化、计算流体力学、图像处理与数据分析、保险精算等。发表学术论文160余篇，其中SCI 140篇。2020年“热耦合流体模型的高效高精度保物理性质算法研究”获自治区科学技术进步奖一等奖【自然科学奖】。现担任中国精算师、中国数学会理事。现主持一个科研计划项目、一个面上项目、一个重点项目。
