崇文讲堂第一百零四期

三维对流扩散方程的差分有限元方法

讲座时间：11月2日16：00—17：00

讲座地点：C4-219

主讲嘉宾：冯新龙

主讲人简介

冯新龙，博士，教授（二级），博士生导师。享受国务院特殊津贴专家，国家重大人才工程特聘教授。研究领域为计算数学、计算流体力学、不确定性量化、人工智能与机器学习等。拥有中国准精算师资格，曾担任中国核学会计算物理学会理事，中国计算数学学会理事，中国数学会理事，目前担任中国高等教育学会教育数学专业委员会常务理事、副秘书长等。主持完成多项国家自然科学基金项目，在国际著名期刊合作发表学术论文百余篇。

讲座内容简介

 In this work, a difference finite element (DFE) method is proposed for solving 3D steady convection-diffusion equations that can maximize good applicability and efficiency of both FDM and FEM. The essence of this method lies in employing the centered difference discretization in the z-direction and the FE discretization based on the P1 conforming elements in the (x,y)- plane. This allows us to solve PDEs on complex cylindrical domains at lower computational costs compared to applying the 3D FEM. We derive the stability estimates for the DFE solution and establish the explicit dependence of H1-error bounds on the diffusivity, convection field modulus, and mesh size. Moreover, a compact DFE method is presented for the similar problems. Finally, numerical examples are provided to verify the theoretical predictions and showcase the accuracy of the considered method.