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

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

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

简介：ItisprovedinthispaperthattheapproximatesolutionofthediscontinuousGalerkinmethoddoesconvergeeventheexactsolutionofthefirstorderhyperbolicequationisdiscontinuous.

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

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

简介：Inthispaper,weuseDaubechiesscalingfunctionsastestfunctionsfortheGalerkinmethod,anddiscussWavelet-GalerkinsolutionsfortheHamilton-Jacobiequations.ItcanbeprovedthattheschemesareTVDschemes.NumericaltestsindicatethattheschemesaresuitablefortheHamilton-Jacobiequations.Furthermore,theyhavehigh-orderaccuracyinsmoothregionsandgoodresolutionofsingularities.

简介：AbstractAsystemofquasilinearcoupledequationswhicharisefromsimulationofcontaminationofgeologicnulearwasteinporousmediaisstudied.We’lldiscussGalerkinmethodforthemodelofcompressibleflowwithmoleculardiffusionanddispersion.Somenewtechniquesareintrocuedtoerroranalysis.Onlyonedimensionalcaseisconsidered.TheoptimalerrorestimateinbothL~2andH~1isproved.Acontributionofthispaperishowthedispersiontermcanbehandled,

简介：

简介：WeconsidertheproblemK(x)uxx=utt,0

简介：Inthispaper,a-posteriorierrorestimatorsareproposedfortheLegendrespectralGalerkinmethodfortwo-pointboundaryvalueproblems.ThekeyideaistopostprocesstheGalerkinapproximation,andtheanalysisshowsthatthepostprocessimprovestheorderofconvergence.Consequently,weobtainasymptoticallyexactaposteriorierrorestimatorsbasedonthepostprocessingresults.Numericalexamplesareincludedtoillustratethetheoreticalanalysis.

简介：ErrorestimatesofGalerkinmethodforKuramoto-Sivashingsky(K-S)equationinspacedimension≥3arederivedinthepaper.Theseresultsfurnishstrongevidenceforthecom-putationofthesolutions.

简介：Inthispaper,theconvergenceandL2estimateoftheGalerkinmethodaregivenforthesteadystateKuramoto-Sivashinsky(K-S)equation.

简介：为在多孔的媒介包括分子的散开和分散的一个可压缩的能溶合的排水量问题的一个联合混合有限元素和不连续的Galerkin方法被调查。那是说，有Raviart-Thomas空间的混合有限元素方法被用于流动方程，和运输一个人被对称的内部惩罚解决不连续的Galerkin(SIPG)近似。把插值和正式就职假设基于设计，superconvergence估计被获得。在分析期间，沿着高斯线的Darcy速度的延期也为集中在Galerkin过程在系数的评估被使用。

简介：Analternating-directionimplicit(ADI)Galerkinnuthodwithmovingfiniteelementspacesisformulatedforaclassofsecond-orderhyperbolicequationsintwospacevariables.AprioriH1-errorestimateisderived.

简介：AnA.D.I.Galerkinschemeforthree-dimensionalnonlinearparabolicintegro-differen-tialequationisstudied.Byusingalternating-direction,thethree-dimensionalproblemisreducedtoafamilyofsinglespacevariableproblems,thecalculationissimplified;byusingalocalapproxima-tionofthecoefficientsbasedonpatchesoffiniteelements,thecoefficientmatrixisupdatedateachtimestep;byusingRitz-Volterraprojection,integrationbypartandothertechniques,theinfluencecomingfromtheintegraltermistreated;byusinginductivehypothesisreasoning,thedifficultycomingfromthenonlinearityistreated.ForbothGalerkinandA.D.I.Galerkinschemesthecon-vergencepropertiesarerigorouslydemonstrated,theoptimalH~1-normandL~2-normestimatesareobtained.

简介：Ahigh-orderleap-frogbasednon-dissipativediscontinuousGalerkintime-domainmethodforsolvingMaxwell'sequationsisintroducedandanalyzed.Theproposedmethodcombinesacenteredapproximationfortheevaluationoffluxesattheinterfacebetweenneighboringelements,withaNth-orderleap-frogtimescheme.Moreover,theinterpolationdegreeisdefinedattheelementlevelandthemeshisrefinedlocallyinanon-conformingwayresultinginarbitrarylevelhangingnodes.ThemethodisprovedtobestableundersomeCFL-likeconditiononthetimestep.Theconvergenceofthesemi-discreteapproximationtoMaxwell'sequationsisestablishedrigorouslyandboundsontheglobaldivergenceerrorareprovided.Numericalexperimentswithhigh-orderelementsshowthepotentialofthemethod.