简介：Abstract.OgrobjectinthisartlcleistodescribetbeGalerklnschemeandnonlin-eaxGalerkinschemefortheapproximationofnonlinearevolutionequations,andtostudythestabilityoftheseschemes.SpatialdiscretizatloncanbepedormedbyeitherGalerklnspectralmethodornonlinearGalerldnspectralmethod;timediscretizatlortisdonehyEulersin.heinewklchisexplicitorimplicitinthenonlinearterms.Accordingtothestabilityanalysisoftheaboveschemes,thestabilityofnonllneexGalerklnmethodisbetterthanthatofGalexklnmethod.

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简介：TheGalerkinandleast-squaresmethodsaretwoclassesofthemostpopularKrylovsubspacemethOdsforsolvinglargelinearsystemsofequations.Unfortunately,boththemethodsmaysufferfromseriousbreakdownsofthesametype:InabreakdownsituationtheGalerkinmethodisunabletocalculateanapproximatesolution,whiletheleast-squaresmethod,althoughdoesnotreallybreakdown,isunsucessfulinreducingthenormofitsresidual.Inthispaperwefrstestablishaunifiedtheoremwhichgivesarelationshipbetweenbreakdownsinthetwometh-ods.Wefurtherillustratetheoreticallyandexperimentallythatifthecoefficientmatrixofalienarsystemisofhighdefectivenesswiththeassociatedeigenvalueslessthan1,thentherestart-edGalerkinandleast-squaresmethodswillbeingreatrisksofcompletebreakdowns.Itappearsthatourfindingsmayhelptounderstandphenomenaobservedpracticallyandtoderivetreat-mentsforbreakdownsofthistype.

简介：Inthispaper,weareconcernedwithuniformsuperconvergenceofGalerkinmethodsforsingularlyperturbedreaction-diffusionproblemsbyusingtwoShishkin-typemeshes.Basedonanestimateoftheerrorbetweensplineinterpolationoftheexactsolutionanditsnumericalapproximation,aninterpolationpost-processingtechniqueisappliedtotheoriginalnumericalsolution.Thisresultsinapproximationexhibitsuperconvergencewhichisuniformintheweightedenergynorm.Numericalexamplesarepresentedtodemonstratetheeffectivenessoftheinterpolationpost-processingtechniqueandtoverifythetheoreticalresultsobtainedinthispaper.

简介：Inthispaper,theminimaldissipationlocaldiscontinuousGalerkinmethodisstudiedtosolvetheellipticinterfaceproblemsintwo-dimensionaldomains.Theinterfacemaybearbitrarysmoothcurves.ItisshownthattheerrorestimatesinL2-normforthesolutionandthefluxareO（h2｜logh｜）andO（h｜logh｜^l/2）,respectively.Innumericalexperiments,thesuccessivesubstitutioniterativemethodsareusedtosolvetheLDGschemes.Numericalresultsverifytheefficiencvandaccuracvofthemethod.

简介：ItisprovedinthispaperthattheapproximatesolutionofthediscontinuousGalerkinmethoddoesconvergeeventheexactsolutionofthefirstorderhyperbolicequationisdiscontinuous.

简介：AD(Alternatingdirection)Galerkinschemesford-dimensionalnonlinearpseudo-hyperbolicequationsarestudied.Byusingpatchapproximationtechnique,ADprocedureisrealized,andcalculation,workissimplified.ByusingGalerkinapproach,highlycomputationalaccuracyiskept.Byusingvariousprioriestimatetechniquesfordifferentialequations,difficultycomingformnon-linearityistreated,andoptimalH^1andL^2convergenceprop-ertiesaredemonstrated.Moreover,althoughalltheexistedADGalerkinschemesusingpatchapproximationarelimitedtohaveonlyoneorderaccuracyintimeincrement,yettheschemesformulatedinthispaperhavesecondorderaccuracyinit.ThisimpliesanessentialadvancementinADGalerkinaualysis.

简介：Akindofcalculatingmethodforhighorderdifferentialsexpandedbythewaveletscal-ingfunctionsandtheintegraloftheirproductusedinGalerkinFEMisproposed,sothatwecanusethewaveletGalerkinFEMtosolveboundary-valuedifferentialequationswithordershigherthantwo.TocombinethismethodwiththeGeneralizedGaussianintegralmethodinwavelettheory,wecanfindthatthismethodhasmanymeritsinsolvingmechanicalproblems,suchasthebendingofplatesandthosewithvariablethickness.Thenumericalresultsshowthatthismethodisaccurate.

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简介：几个Galerkin-Petrov方法，包括的多项式搭配和分析元素的集中在Dirichlet空间的Toeplitz操作员的搭配方法，被建立。特别地，如果基础和测试功能拥有某些圆形的对称，如此的方法收敛，这被显示出。给词调音：GalerkinPetrov方法；多项式搭配；分析元素搭配；Toeplitz操作员；Dirichlet空间

简介：Weperformanalysisforafiniteelementsmethodappliedtothesingularself-adjointproblem.Thismethodusescontinuouspiecewisepolynomialspacesforthetrialandthetestspaces.WefitthetrialpolynomialspacebypiecewiseexponentialsandweapplysoexponentiallyfittedGalerkinmethodtosingularself-adjomtproblembyapproximatingdrivingtermsbyLagrangepiecewisepolynomials,linear,quadraticandcubic.Wtmeasuretheerroeinmaxnorm.Weshowthatmethodisoptimalofthefirstorderintheerrorestimate,WealsogivenumericalresultsfortheGalerkinapproximation.

简介：在这篇论文，我们在场一个不连续的Galerkin(DG)方法基于为解决在3-dimensional上从一个magnetohydrodynamics模型产生的一个第四顺序的卷屈方程的Nedelec有限元素空间围住Lipschitz多面体。我们证明方法为包含一个第四顺序的卷屈操作员的一个模型问题有最佳的错误估计。而且，在2种尺寸的一些数字结果被介绍验证理论结果。

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简介：为Sobolev方程，我们在场一个新数字计划基于一个修改弱Galerkin有限元素方法，微分操作员被部分被弱形式通过平常的集成在接近。特别地，数字方法允许不连续的有限元素功能的使用和元素的任意的形状。在分离H1和L2标准的最佳的顺序错误估计为相应修改弱Galerkin有限元素答案被建立。最后，一些数字结果被给验证理论结果。[从作者抽象]

简介：NonlinearGalerkinmethodsarenewschemesforintegratingdissipativesystems:Inthepresentpaper,weobtaintheestimatestotherateofconvergenceofsuchmethodsforKuramoto-Sivashinskyequations.Inparticular,byanillustrativeexample,weshowthatnonlinearGalerkinmethodsconvergefasterthantheusualGalerkinmethod.

简介：Designofenergeticmaterialsisanexcitingareainmechanicsandmaterialsscience.Energeticcompositematerialsareusedaspropellants,explosives,andfuelcellcomponents.Energyreleaseinthesematerialsareaccompaniedbyextremeevents:shockwavestravelattypicalspeedsofseveralthousandmeterspersecondandthepeakpressurescanreachhundredsofgigapascals.Inthispaper,wedevelopareactivedynamicscodeformodelingdetonationwavefeaturesinonesuchmaterial.Thekeycontributioninthispaperisanintegratedalgorithmtoincorporateequationsofstate,Arrheniuskinetics,andmixingrulesforparticledetonationinaTaylor–Galerkinfiniteelementsimulation.Weshowthattheschemecapturesthedistinctfeaturesofdetonationwaves,andthedetonationvelocitycompareswellwithexperimentsreportedinliterature.

简介：在这篇文章，我们为当模特儿的海军司烧方程的数字答案讨论一个新完整的分离计划粘滞不可压缩的流动。这个计划用混合有限元素和曲柄由非线性的Galerkin方法组成--Nicolson方法。下次，我们提供相应于这个计划的数字答案的秒顺序集中精确性。与平常的Galerkin计划相比，这个计划能在一样的集中精确性下面节省大量计算时间。(作者摘要)8个裁判员。

简介：Inthispaper,aunifiedmodelfortime-dependentMaxwellequationsindispersivemediaisconsidered.Thespace-timeDGmethoddevelopedin[29]isappliedtosolvetheunderlyingproblem.UnconditionalL2-stabilityanderrorestimateoforderOτr+1+hk+1/2areobtainedwhenpolynomialsofdegreeatmostrandkareusedforthetemporaldiscretizationandspatialdiscretizationrespectively.2-Dand3-Dnumericalexamplesaregiventovalidatethetheoreticalresults.Moreover,numericalresultsshowanultra-convergenceoforder2r+1intemporalvariablet.

简介：在这份报纸，我们由一种指数地适合的技术为一个维的不可思议地使不安的传送对流散开问题学习本地不连续的Galerkin(LDG)方法。我们关于小散开参数在精力标准证明方法是一致地一阶的会聚。

简介：ThispaperproposesageometricallynonlineartotalLagrangianGalerkinmeshfreeformulationbasedonthestabilizedconformingnodalintegrationforefficientanalysisofsheardeformablebeam.Thepresentnonlinearanalysisencompassesthefullygeometricnonlinearitiesduetolargedeflection,largedeformationaswellasfiniterotation.Theincrementalequilibriumequationisobtainedbytheconsistentlinearizationofthenonlinearvariationalequation.TheLagrangianmeshfreeshapefunctionisutilizedt...