各向異性元的收斂性與誤差估計(jì)問題的研究.pdf

1、中南大學(xué)碩士學(xué)位論文各向異性元的收斂性與誤差估計(jì)問題的研究姓名：張翠翠申請學(xué)位級別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：鄭洲順20071128ABSTRACTThisthesisisdevotedtotheproblemsofanisotropicfiniteelementsconvergenceofvicoelasticequationandparabolicintegrodifferentialequationandtheerroresti

2、matesofvariablecoe街cientparabolicequationwithanisotropicmoving鰣dsfiniteelementmethodsmainlyItiscomposedofsixchaptersInchapter1，itiSsummarizedaboutthehistoricalbackgroundandthepresentprogressofanisotropicfiniteelementsAtt

3、hesametime，themainworkofthepaperisconcludedInchapter2，thebasicknowledgeiSintroduced，whichcanbeusedinthefollowingchaptersInchapter3，wediscusstheconvergenceofvicoelasticequationwithanisotropicnonconformingelementwegetme厶er

4、rorestimateusingtheanisotropicinterpolationtheoremtheerrorestimatesofthefiniteelementsolutionandsuperclosepropertyofvicoelasticequationAlsowegetthesuperconvergenceresultonthecentralpointofelementofvicoelasticequationusin

5、gthepolynomialtestmethodInchapter4，wediscusstheconvergenceofparabolicintegrodifferentialequationwithanisotropictripledimension1inearelementFirstlyweprovetheintegralinequalityoftheanisotropicgridswithanewsimlplemethodBili

6、nearLemma，andweget厶errorestimatewithBramble—HilbertLemmaTheerrorestimatesofthefiniteelementsolution，superclosepropertyandglobalsuperconvergencepropertyofparabolicintegrodifferentialequationarediscussedandderivedAtthesame

7、timeWegetthesuperconvergenceresultonthecentralpointofelementofparabolicintegro—differentialequationusingthepolynomialtestmethodInchapter5，wediscusstheerrorestimatesofvariablecoefficientparabolicequationwithanisotropicmov

8、inggddsFirstlythepropertyofellipticprojectionisprovedontheanisotropic酊dsWegettheerrorestimatesformulaoftheenergynormand厶一norm，andtheoptimalenergynormand厶一normerrorestimatesarederivedInchapter6，alltheworkofthisthesisiSsum