Cahn-Hilliard方程的高精度數(shù)值方法.pdf

1、中國海洋大學(xué)碩士學(xué)位論文CahnHilliard方程的高精度數(shù)值方法姓名：趙睿申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：謝樹森20090601HighOrderAccurateNumericalMethodsforCahn—HilliardEquationsAbstractCahnHilliardequationisanimportantforthordernonhneardiffusionequation，Sincewecannoth

2、opeforanalyticalsolutions，wemustresorttonumericalmethodstosolvetheCahn—HilliardequationEvennumericalsolutionsfirenoteasytoobtainThisispartlybecausethestrongnonlinearbehaviorandthedependenceofthesolutionontheinitialdatau(

3、z，0)isverysensitiveOurmainworkisthatdiscussthenumericalsolutionsFirstinpreface，weintroducethebackgroundsandsignificancesofCahnHillifirdequation，thepresentstudiesofhomeandabroadreserchersaresummarized，introducesmainideaof

4、ourwork，spreadoutrudimentaryknowledgethatbeusedThemainbodyofthearticlecomposedofthreechapters，whichstudyinitialboundaryvalueproblemofCalmHilliardequationandakindofCahn—Hillifirdequationwithmethodshavehighdegreeofaccuracy

5、ThechaptertwoconsiderstheonedimensioninitialboundaryvalueproblemofCahn—HilliardequationItusingBsplineGalerkinmethoddiscretesthespacialvfiriateConsequentlyitconstructsthefiniteelementformatsforthisfourthorderequation，then

6、provesthetwofamouspropertiesthatthetotalmassconservedandthetotalfreeener93rdecreaseswithtimeWeprovesthatapproximatesolutionisboundedatmaximumnormbySobolevlemmaandobtainsO(h4T2)errorsThechapterthree，weconstructsthetwokind

7、scompactfinitedifferenceschemeforCahl3HilliardequationThetwonewschemesalsoinherittheconservationofmasspropertiesThen，bymethodofinductiveassumption，weprovethestabilityandconvergenceofthenumencMsolution，theorderoferrorispf