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崇文講堂第一百零四期

三維對流擴(kuò)散方程的差分有限元方法

講座時(shí)間：11月2日16：00—17：00

講座地點(diǎn)：C4-219

主講嘉賓：馮新龍

主講人簡介

馮新龍，博士，教授（二級），博士生導(dǎo)師。享受國務(wù)院特殊津貼專家，國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。擁有中國準(zhǔn)精算師資格，曾擔(dān)任中國核學(xué)會計(jì)算物理學(xué)會理事，中國計(jì)算數(shù)學(xué)學(xué)會理事，中國數(shù)學(xué)會理事，目前擔(dān)任中國高等教育學(xué)會教育數(shù)學(xué)專業(yè)委員會常務(wù)理事、副秘書長等。主持完成多項(xiàng)國家自然科學(xué)基金項(xiàng)目，在國際著名期刊合作發(fā)表學(xué)術(shù)論文百余篇。

講座內(nèi)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 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.