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1、DevelopingWeakGalerkinFiniteElementMethodsfortheWaveEquationYunqingHuang,1JichunLi,2DanLi31HunanKeyLaboratoryforComputationandSimulationinScienceandEngineering,XiangtanUniversity,China2DepartmentofMathematicalSciences,UniversityofNevadaLasVegas,LasVegas,Nevada3
2、HunanKeyLaboratoryforComputationandSimulationinScienceandEngineering,XiangtanUniversity,ChinaReceived6September2016;revised21November2016;accepted21November2016PublishedonlineinWileyOnlineLibrary(wileyonlinelibrary.com).DOI10.1002/num.22127Inthisarticle,weexten
3、dtherecentlydevelopedweakGalerkinmethodtosolvethesecond-orderhyper-bolicwaveequation.ManynicefeaturesoftheweakGalerkinmethodhavebeendemonstratedforelliptic,parabolic,andafewothermodelproblems.ThisistheinitialexplorationoftheweakGalerkinmethodforsolvingthewaveeq
4、uation.HerewesuccessfullydevelopedandestablishedthestabilityandconvergenceanalysisfortheweakGalerkinmethodforsolvingthewaveequation.Numericalexperimentsfurthersupportthetheoreticalanalysis.©2017WileyPeriodicals,Inc.NumerMethodsPartialDifferentialEq000:000000,20
5、17Keywords:finiteelementmethod;second-orderhyperbolicequation;waveequation;weakGalerkinI.INTRODUCTIONTheweakGalerkin(WG)finiteelementmethod(FEM)wasrecentlyintroducedbyWangandYe[1,2]forsolvingsecond-orderellipticproblems[3].ThenovelideaofWG-FEMistointroduceweakfun
6、ctionsandweakderivativeswithunknownsdefinedbothinsideelementsandonelementinterfaces.HencetheWGmethodismoreflexibleinhandlingproblemswithcomplexgeometriesanddiscontinuoussolutions.TheimplementationprocessoftheWGmethodforsecond-orderellipticequationswithmoregeneral
7、finiteelementpartitionshasbeenexplainedin[4].Accordingto[1,2],theWGmethodallowsarbitraryshapeofpolygonsfortwo-dimensionaldomainandpolyhedraforthree-dimensionaldomain,whichmakesmeshgenerationmoreflexible.AnotheruniquefeatureofWGmethodisthattheformulationisparamete
8、r-free,unlikemanydiscontinuousCorrespondenceto:JichunLi,DepartmentofMathematicalSciences,UniversityofNevadaLasVegas,LasVegas,NV(e-mail:jichun.li@unlv.edu)Contractgrantsponso
