题    目：Theory and Calculation of Difference Finite Element Method

主讲人：冯新龙 教授

单    位：新疆大学

时    间：2025年11月1日 9:30

腾讯ID：339-858-660

摘    要：In this work, a difference finite element (DFE) method is proposed for solving 3D steady PDEs that can maximize good applicability and efficiency of both FDM and FEM. The essence of this method lies in employing the FD discretization in the $z$-direction and the FE discretization based on the $P_1$ 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 $H_1$ error bounds on the diffusivity, convection field modulus, and mesh size. Moreover, a compact DFE method is presented for the similar problems. Finally, we provide numerical examples to verify the theoretical predictions and showcase the accuracy of the considered method.

简    介：冯新龙，博士，二级教授，博士生导师。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。主持完成多项国家自然科学基金项目，在SIAM、IEEE系列国际著名期刊合作发表学术论文百余篇。