標(biāo)題：Compact difference finite element method for convection-diffusion equations on cylindrical domains
報(bào)告時(shí)間：2024年8月17日(星期六)16：30-17：30
報(bào)告地點(diǎn)：人民大街校區(qū)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院二樓會(huì)議室
主講人：馮新龍
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告內(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 above problems. Finally, we provide numerical examples to verify the theoretical predictions and showcase the accuracy of the proposed method
主講人簡(jiǎn)介：
馮新龍，二級(jí)教授，博士生導(dǎo)師。享受?chē)?guó)務(wù)院特殊津貼專(zhuān)家，教育部重大人才工程特聘教授。研究領(lǐng)域?yàn)橛?jì)算數(shù)學(xué)、計(jì)算流體力學(xué)、不確定性量化、人工智能與機(jī)器學(xué)習(xí)等。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，中國(guó)數(shù)學(xué)會(huì)理事，目前擔(dān)任中國(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。曾榮獲自治區(qū)自然科學(xué)獎(jiǎng)一等獎(jiǎng)，新疆青年科技獎(jiǎng)等。主持完成10余項(xiàng)國(guó)家級(jí)和省部級(jí)科研項(xiàng)目。在國(guó)際著名期刊合作發(fā)表學(xué)術(shù)論文100余篇。
