对流占优扩散问题特征混合有限元方法的一致估计

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1、GVADmZDfluxhavebeenobtained.However,theseerrorestimateswereprovedviatheintro-ductionofthemixedellipticprojectionwhoseapproximationpropertydependsonthesmallparameterε,thustheconstantsintheseerrorestimatesalsodependonε.Whenεtendstozero,itwillblowupasthelowerboundofthediffu

2、sionapproachestozero.Forderivingε-uniformestimates,inthispaper,westilladoptthecharacteristics-mixedfiniteelementschemesforconvection-dominateddiffusionequationswithaperiodicboundarycondition.ThemixedellipticprojectionsarereplacedbytheRaviart-Thomasprojectionandtheinterpolat

3、ionoperatorsintheerrorderivation,thereforetheuniformerrorestimatesfortheunknownfunctionanditsfluxarede-rived.Thegenericconstantsintheerrorestimatesdonotexplicitlydependonε,butdependlinearlyoncertainSobolevnormsofthetruesolution.Inthederivationofthefirstcharacteristics-mixed

4、method,weobtaintheoptimallyuniformestimateswhentheCourantnumberislessthanunity.Combiningtheestimateswiththesta-bilityestimatesofthetruesolution,weprovetheseconstantsdependonlyontheinitialandtherightsidedata.Numericalexperimentsarepresentedtoconfirmourtheoreticalfindings.Key

5、words:Advection-dominateddiffusionequations,Characteristics-mixedfiniteelementmethod,Uniformerrorestimates,Numericalexperiments.SubjectClassification:O241.824GVADmZD7&8)"2℄`~?∂Ω`?.eΩ⊂RdS*.*(0,T]}A%℄zx^^E
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