投影型插值的新的特殊性質(zhì)及其在高次有限元中的應(yīng)用.pdf

1、湖南師范大學(xué)碩士學(xué)位論文投影型插值的新的特殊性質(zhì)及其在高次有限元中的應(yīng)用姓名：祝儷華申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：朱起定20050301II湖南師范大學(xué)2005屆碩士學(xué)位論文ABSTRACTInthisthesis，somenewspecialpropertiesoftheprojectiontypeinterpolationarestudiedbased0nthelobattoexpansionofthefunctiona

2、ndtheoriginaltheoryoftheprojectiontypeinterpolationAnditisprovedthatthenewtypeinterpolationistheoptimalinterpolationinthecalculusofhighdegreefiniteelementsFirstly，anewerrorestimatemodelpointwiseerrorestimateoftheprojecti

3、ontypeinterpolationispresentedThedegreeofinterpolationpolynomial七canincreasedynamicallyandtherelationbetweenerrorcoefficientsandkisshowedaccuratelySecondlyarecursivecalculationmethodandtheapproximationcurveoferrorpolynom

4、ia1Ak(z)aregivenflUt；whichshowtheuniformapproximationofprojectiontypeinterpolationFinallylanewresultisobtainedthattheprojectiontypeinterpolationistheoptimalinterpolationinthecalculusofhigh—degreefiniteelements，whichisver

5、ifiedbyanumericalexampleforveriablecoefficientstwo—pointboundaryvalueproblemThusanewmethodfortheerrorestimationofthefiniteelementsolutionisproposedKeywords：finiteelement，projectioninterpolation，opti—realinterpolation，poi