兩類拋物方程的最小二乘特征混合元法.pdf

1、長沙理工大學碩士學位論文兩類拋物方程的最小二乘特征混合元法姓名：劉衍瓊申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：張宏偉20090401AbstractABSTRACTTherehasbeenagreatdevelopmentforthemethodoffiniteelementsince1950sinpracticalapplication，forexample：least—squaresmixedfiniteelementmethod

2、，characteristicsfiniteelementandmovingmeshfiniteelementThesemethodshavebeengenerallyappliedinmanyindustryfieldsandmanyproblemsinreallifehavebeensolvedTheLeastsquaresmixedfiniteelementmethodshavebeenformulatedtosolveconve

3、ctiondiffusionparabolicdifferentialequationsTheadvantageofthismethodsisthatitisnotsubjecttotheLBBconditionTheconvergenceanalysisshowedthattheleastsquaresmixedelementschemesyieldtheapproximatesolutionwithoptimalaccuracyin

4、H(div；Q)xH1(Q)Themaintaskinthispaperistosolveconvection—diffusionparabolicequationsbymakinguseofthemethodsofleastsquaresmixedfiniteelement，characteristicsfiniteelementandmovingmeshfiniteelementAccordingtotheactualneedsof

5、problemforconvection—diffusionparabolicequations，togetherleast—squaresmixedfiniteelementschemeswiththemethodofcharacteristics，wediscusstwoleastsquarescharacteristicsmixedfiniteelementproceduresforonekindofconvection—domi

6、natedparabolicequationsOntheotherhand，theleastsquarescharacteristicsmixedfiniteelementschemewithmovingmeshisformulatedtosolvefirst—ordertimedependentconvectiondiffusionsystemsErrorestimateshowthatthemethodhaveoptimalconv

7、ergentrateinsomesenseItsmaincontentsareasfollows：InthefirstchapterprefacegivesthebackgroundandthestatusofrecentresearchofthefiniteelementmethodInthe爭ecpndchaptersomenotesandthreekindsoffiniteelementmethodarepresentedandw

8、ewilluseinthepaperInthethjrdchapterwestudyonekindofconvection—dominatedparabolicdifferentialequationbythemethodofleast—squarescharacteristicsmixedfiniteelementandgetoptimalestimationfortwodifferentleast—squarescharacteri