四階方程的特征線混合有限元方法.pdf

1、內(nèi)蒙古大學(xué)碩士學(xué)位論文四階方程的特征線混合有限元方法姓名：杜敏申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：李宏20090501THECHARACTERISTICMIXEDFINITEELEMENTMETHODSFORTHEFOURORDEREQUATIONSABSTRACTCharacteristicmixedfiniteelementmethodsforfourorderequationsarediscussedinthispaperT

2、hemainfeaturesofthesemethodsarethatthehighorderequationsareloweredbythemixedfiniteelementmethodfirstlyandtimederivativeisdiscretizedbythecharacteristicmethodThenthelowerequationsarediscretizedbythecontinuousfiniteelement

3、methodsForakindoffourthorderparabolicequationsr’w以麓霧Q(0，卅，QaQ(0，丁】(003)usingmixedfinite砂=△砂forloweringthehighorderequation，andthecharacteristicmethodin九UV砂ofequationareusedThecharacteristicmixedfiniteelementschemearegive

4、nExistenceanduniqueness，stabilityanderrorestimatesofthefiniteelementsolutionareprovedForakindofonedimensionalfourorderequations，r‰～z—n乏基礎(chǔ)a三二(0，刀，(0，印，Q(004)usingmixedfinitep=Ut—Uzzforloweringthehighorderequation，discreti

5、zedtimederivativewithEulermethodandcharacteristicmethod，anddiscretizedspacevariableUSingcontinuousfiniteelementmethodRelatedestimationsofthefiniteelementsolutionareprovedKEYWORDSFourthOrderParabolicDifferentialEquation；C