二維二階橢圓問題的多尺度間斷有限元方法.pdf

1、南開大學(xué)碩士學(xué)位論文二維二階橢圓問題的多尺度間斷有限元方法姓名：邢中寶申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：由同順20090601AbstractiiAbstractManyproblemsoffundamentalandpracticalimportancesuchascompositemate—rials，porousmedia，andturbulenttransportinhighReynoldsnumberflowshave

2、multiscalesolutionsSolvingsuchkindofmulti—scalePDEsbythestandardGalerkinfiniteelementmethoddemandsfinemeshgridandmassstorageMultiscalefiniteelementmethod，whichwaspromotedbyTYHou，isusedtoefficientlycapturethelargescalebeh

3、aviorofthesolutionbymultiscalebasefunctionswithoutresolvingallthesmallscalefeaturesbuthasaaloworderofenDrestimateInthispaperamulti—scalediscontinuousGalerkinmethodisdesignedtoobtainthelargescMefeaturesandimprovetheordero

4、ferrorestimateThemultiscalefiniteelementmethodisintroducedatfirstinthispaperandthenthenumericalformulaofmultiscaleBabu謄kaZldmaldiscontinuousGalerkinmethodfollowsOurnumericalexperimentsshowthat，themulti—scalediscontinuous

5、GalerkinmethodCanachieveatleastfiftherrororderfor2Dellipticmulti—scaleproblemsMean—while，itinheritstheadvantagesofbothfinitemulti—scalemethodandthediscontinuousGalerkinmethod。Keywords：multi—scalePDEmultiscalefiniteelemen