永利app官网登录入口栏目导航 - 永利app官网登录入口

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 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.

冯新龙，新疆大学数学与系统永利app官网登录入口栏目导航二级教授，博士生导师。研究领域包括计算数学、计算流体力学、不确定性量化、人工智能与机器永利app官网登录入口栏目导航等。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、中国数学会理事等。曾荣获永利app官网登录入口栏目导航部高等院校青年教师奖、自治区科学技术进步奖等。入选永利app官网登录入口栏目导航部重大人才计划、享受国务院特殊津贴专家等。主持完成10余项永利app官网登录入口栏目导航级和省部级自然科学基金项目。已在SIAM、IEEE等国际著名期刊合作发表论文100余篇。