數(shù)學(xué)與統(tǒng)計(jì)學(xué)院學(xué)術(shù)報(bào)告預(yù)告：Difference finite element method for 3D convection-diffusion equations

報(bào)告題目：Difference finite element method for 3D convection-diffusion equations

報(bào) 告 人：馮新龍

報(bào)告時(shí)間：11月17日10：00

報(bào)告地點(diǎn)： 蓮花街校區(qū)惟德樓315會(huì)議室

報(bào)告人簡(jiǎn)介：馮新龍，博士，教授，博士生導(dǎo)師。享受?chē)?guó)務(wù)院特殊津貼專(zhuān)家，國(guó)家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，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。主持完成多項(xiàng)國(guó)家自然科學(xué)基金項(xiàng)目，在國(guó)際著名期刊合作發(fā)表學(xué)術(shù)論文百余篇。

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 similar problems. Finally, numerical examples are provided to verify the theoretical predictions and showcase the accuracy of the considered method.

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數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
2024年11月14日