Compact difference finite element method for 3D convection-diffusion equations
報告人簡介
馮新龍，新疆大學教授，博士生導師。博士畢業于西安交通大學數學專業。曾在韓國首爾國立大學、香港浸會大學、巴西巴拉那聯邦大學、加拿大阿爾伯塔大學從事博士后研究工作和短期訪問。擁有中國準精算師資格，曾擔任中國核學會計算物理學會理事、中國計算數學學會理事，目前擔任中國數學會理事、中國高等教育學會教育數學專業委員會常務理事等。曾榮獲教育部高等院校青年教師獎、自治區科學技術進步獎一等獎和二等獎以及新疆青年科技獎等。擔任“科學計算與機器學習及應用”自治區天山創新團隊負責人。主持完成近20項國家級和省部級自然科學基金項目。已在SIAM系列、MCOM、CMAME、JCP、IJNME、JSC等國際著名期刊合作發表學術論文200余篇。
內容簡介
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 $P_1$ 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.
