一階雙曲型方程的時空間斷全離散有限元的收斂性.pdf

1、湖南師范大學(xué)碩士學(xué)位論文一階雙曲型方程的時空間斷全離散有限元的收斂性姓名：張自力申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：陳傳淼20050301O2AbstractBasirlgonthediscontinuousfinitee]ementidealforordinarydifferen—tim，wehavetakenadvantageofenergymethod，orthogonalanalysisinele‘mentlconstru

2、ctespecialorthogonalanalyzeandtensorproductdecomposelsimplyproveconvergenceofspacetimediscontinuousfiniteelementofonorderhy—perholicsystemWehavehadfull—degreeerrorestimationNumericalexper—imentationhavenotonlyprovedtheth

3、eoreticalresultbutalsofoundoutsupcrconvergenceofhigherorderMainresultfollows：(1)AccordingtotheidealofRorthogonalexpand，tensorproductde—composeandthemethodofenergy，wehavesimplyprovedone—orderhyper—bolicsystemsproblemtimes

4、pacediscontinuousfiniteelementsolutionU∈驢os“(fortimespaceo，ldegreB、spacemdegree)havefulldegreeconvergence：|I(u—U)llSC(T，)(^“1kP1)WhereSkispdegreefiniteelementspaceintimeS^ism—degreefiniteelementspaceinspaceThismethodisgo

5、odformultiplicity—dimensiontoor2)ProfassorChuanmiacChenhasprovedsupereonvergence扯pl1orderRadaupointsintheelementAtthefirsttime，numericalexperimentationprovehassimilarsuperconvergenceatPlandk1degreeRadaupoints’productpoin

6、tsforone—orderhyperbolicproblembyusingdiscontinuousfiniteelementmethodButtheresulthasnotbeenprovedintheoryyetKeywords：oneorderhyperbolicsystems，discontinuousfiniteelementtensorproductdecomposelfull—degreeerrorestimation，