Compact difference finite element method for 3D convection-diffusion equations
報(bào)告人簡(jiǎn)介
馮新龍，新疆大學(xué)教授，博士生導(dǎo)師。博士畢業(yè)于西安交通大學(xué)數(shù)學(xué)專(zhuān)業(yè)。曾在韓國(guó)首爾國(guó)立大學(xué)、香港浸會(huì)大學(xué)、巴西巴拉那聯(lián)邦大學(xué)、加拿大阿爾伯塔大學(xué)從事博士后研究工作和短期訪(fǎng)問(wèn)。擁有中國(guó)準(zhǔn)精算師資格，曾擔(dān)任中國(guó)核學(xué)會(huì)計(jì)算物理學(xué)會(huì)理事、中國(guó)計(jì)算數(shù)學(xué)學(xué)會(huì)理事，目前擔(dān)任中國(guó)數(shù)學(xué)會(huì)理事、中國(guó)高等教育學(xué)會(huì)教育數(shù)學(xué)專(zhuān)業(yè)委員會(huì)常務(wù)理事等。曾榮獲教育部高等院校青年教師獎(jiǎng)、自治區(qū)科學(xué)技術(shù)進(jìn)步獎(jiǎng)一等獎(jiǎng)和二等獎(jiǎng)以及新疆青年科技獎(jiǎng)等。擔(dān)任“科學(xué)計(jì)算與機(jī)器學(xué)習(xí)及應(yīng)用”自治區(qū)天山創(chuàng)新團(tuán)隊(duì)負(fù)責(zé)人。主持完成近20項(xiàng)國(guó)家級(jí)和省部級(jí)自然科學(xué)基金項(xiàng)目。已在SIAM系列、MCOM、CMAME、JCP、IJNME、JSC等國(guó)際著名期刊合作發(fā)表學(xué)術(shù)論文200余篇。
內(nèi)容簡(jiǎn)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.
