冯新龙，新疆大学教授，博士生导师。博士毕业于西安交通大学数学专业。曾在韩国首尔国立大学、香港浸会大学、巴西巴拉那联邦大学、加拿大阿尔伯塔大学从事博士后研究工作和短期访问。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，目前担任中国数学会理事、中国高等教育学会教育数学专业委员会常务理事等。曾荣获教育部高等院校青年教师奖、自治区科学技术进步奖一等奖和二等奖以及新疆青年科技奖等。担任“科学计算与机器学习及应用”自治区天山创新团队负责人。主持完成近20项国家级和省部级自然科学基金项目。已在SIAM系列、MCOM、CMAME、JCP、IJNME、JSC等国际著名期刊合作发表学术论文200余篇。
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 $P_1$ 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.
