简介:Abstract.OgrobjectinthisartlcleistodescribetbeGalerklnschemeandnonlin-eaxGalerkinschemefortheapproximationofnonlinearevolutionequations,andtostudythestabilityoftheseschemes.SpatialdiscretizatloncanbepedormedbyeitherGalerklnspectralmethodornonlinearGalerldnspectralmethod;timediscretizatlortisdonehyEulersin.heinewklchisexplicitorimplicitinthenonlinearterms.Accordingtothestabilityanalysisoftheaboveschemes,thestabilityofnonllneexGalerklnmethodisbetterthanthatofGalexklnmethod.
简介:IntroductionTheconceptsofInertialManifold(IM)[1]andApproximateInertialManifold(AIM)[2]fordissipativepartialdifferentialequati...
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.
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.
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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:Inthispaper,aunifiedmodelfortime-dependentMaxwellequationsindispersivemediaisconsidered.Thespace-timeDGmethoddevelopedin[29]isappliedtosolvetheunderlyingproblem.UnconditionalL2-stabilityanderrorestimateoforderOτr+1+hk+1/2areobtainedwhenpolynomialsofdegreeatmostrandkareusedforthetemporaldiscretizationandspatialdiscretizationrespectively.2-Dand3-Dnumericalexamplesaregiventovalidatethetheoreticalresults.Moreover,numericalresultsshowanultra-convergenceoforder2r+1intemporalvariablet.
简介:ThispaperproposesageometricallynonlineartotalLagrangianGalerkinmeshfreeformulationbasedonthestabilizedconformingnodalintegrationforefficientanalysisofsheardeformablebeam.Thepresentnonlinearanalysisencompassesthefullygeometricnonlinearitiesduetolargedeflection,largedeformationaswellasfiniterotation.Theincrementalequilibriumequationisobtainedbytheconsistentlinearizationofthenonlinearvariationalequation.TheLagrangianmeshfreeshapefunctionisutilizedt...