简介：这篇论文在各向异性的矩形的网孔的班上处理双线性的有限元素的高精确性分析。各向异性的网孔上的反的不平等被建立。超级结束和超级集中被获得因为第二订椭圆形的问题。数字测试被给，它与我们的理论分析与一致。

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简介：AmodificationofafiniteelementmethodofDouglasandRobertsforapproximatingthesolutionoftheequationsdescribingcompressiblemiscibledisplacementinaporousmediumisproposedandanalyzed.ThepressureistreatedbyaparabolicmixedfiniteelementmethodusingaRaviart-Thomasspaceofindexroveraquasiregularpartition,AnextensionoftheDarcyvelocityalongGausslinesisusedintheevaluationofthecoefficientsintheGalerkinprocedurefortheconcentration.Asimplecomputationalprocedureallowsthesuperconvergencepropertyofthefluidvelocitytoberetainedinourtotalalgorithm.

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

简介：这份报纸从三个方面为非线性的Hamiltonian系统涉及有限元素方法：精力，symplicity，和全球错误的保存。学习有限元素方法的symplecticity，我们使用所有分析方法而非通常使用的代数学的方法。我们在节点t证明集中的顺序最佳[n]在中间长的时间并且表明高精确性的symplecticity。证明强烈取决于superconvergence分析。数字实验证明建议方法能保存精力很好并且能也在长时间使全球轨道错误小。[从作者抽象]

简介：ConsiderL2-projectionuhofuton-degreefiniteelementspaceonone-dimensionaluniformgrids.TwodifferentclassesoftheorthogonalexpansioninanelementforconstructingasuperclosetofunctionuhareproposedandthensuperconvergenceforbothuhandDuhareproved.Whennisoddandnoboundaryconditionsareprescribed,thenuhisofsuperconvergenceatn+1orderGausspointsGn+1ineachelement.Whennisevenandfunctionvaluesontheboundaryareprescribed,thenuhisofsuperconvergenceatn+1orderpointsZn+1ineachelement.Iftheotherboundaryconditionsaregiven,thentheconclusionsarevalidinallelementsthatitsdistancefromtheboundary≥ch|lnh|.Theaboveconclusionsarealsovalid.forn-dergreerectangularelementQ1（n）.

简介：Somesuperconvergenceresultsofgeneralizeddifferencesolutionforellipticboundaryvalueproblemaregiven.Itisshownthatoptimalpointsofthestressesforgeneralizeddifferencemethodarethesameasthatforfiniteelementmethod.

简介：ThepurposeofthispaperistostudythesuperconvergencepropertiesofRitz-Volterraprojection.ThroughconstructionanewtypeofGreenfunctionandmakinguseofitspropertiesandtheprincipleofduality,thepaperprovesthattheRitz-Volterraprojectiondefinedonr-1orderfiniteelementspacesofLagrangetypeinoneandtwospacevariablecasespossessesO(h2r~2)orderandO(h4+1|Inh|)ordernodalsuperconvergence,respectively,andthesametypeofsuperconver-genceresultsaredemonstratedforthesemidiscretefinitedementapproximatesolutionsofSoboleve-quations.

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简介：Superconvergencestructuresforrectangularandtriangularfiniteelementsaresummarized.TwodebatableissuesinZhu''spaper[18]arediscussed.Asuperclosepolynomialtocubictriangularfiniteelementisconstructedbyareacoordinate.

简介：集中和为在一个维的设定的一个不可思议地使不安的模型问题的不连续的Galerkin(DG)方法的超级集中性质被学习。由与DG答案的适当地选择的数字踪迹，存在和唯一使用DG方法，最佳的顺序L₂错误界限，和2p+i顺序数字踪迹斧子的超级集中建立了。数字结果显示DG方法不甚至在一致网孔下面生产任何摆动。数字实验证明在一致网孔下面，获得数字踪迹的一致超级集中似乎不可能。不过，对所谓的Shishkin类型的实现的感谢协调，一致2p+1顺序超级集中数字地被观察。

简介：在这篇论文，超级集中结果为问题管理了由的边界控制的一个班被导出司烧方程。我们为控制和州的近似导出超级集中结果。超级集中结果上的底，我们获得asymptoticallyexact后验错误估计。

简介：InthispapertheWilsonnonconformingfiniteelementisemployedtosolveSobolevandviscoelasticitytypeequations.Bymeansofpost-processingtechnique,globalsuperconvergenceestimatesareobtainedforquasi-uniformrectangularmeshes.Finally,anerrorcorrectionschemeispresented.

简介：在这篇论文，我们为一个模型调查先验的错误估计和超级集中性质最佳的控制问题双线性打申请，它包括某参数评价。州、有肋骨是由片的discretized明智的线性功能和控制被片接近明智的经常的功能。我们为控制和州的近似导出先验的错误估计和超级集中分析。我们也在状态附近给最佳的L2标准错误估计和几乎最佳的L^∞-norm估计并且有肋骨。结果能乐意地被使用在如此的最佳的控制问题的适应有限元素近似构造后验错误评估者。

简介：Superconvergenceofthemixedfiniteelementmethodsfor2-dMaxwellequationsisstudiedinthispaper.Twoorderofsuperconvergentfactorcanbeobtainedforthek-thNedelecelementsontherectangularmeshes.

简介：Inthispaper,weconsiderthelocaldiscontinuousGalerkinmethod(LDG)forsolv-ingsingularlyperturbedconvection-diffusionproblemsinone-andtwo-dimensionalset-tings.TheexistenceanduniquenessoftheLDGsolutionsareverified.Numericalex-perimentsdemonstratethatitseemsimpossibletoobtainuniformsuperconvergencefornumericalfluxesunderuniformmeshes.Thankstotheimplementationoftwo-typedif-ferentanisotropicmeshes,i.e.,theShishkinandanimprovedgrademeshes,theuniform2p+1-ordersuperconvergenceisobservednumericallyforbothone-dimensionalandtwo-dimensionalcases.

简介：Inthispaper,wepresenttheleast-squaresmixedfiniteelementmethodandinvestigatesuperconvergencephenomenaforthesecondorderellipticboundary-valueproblemsovertriangulations.OnthebasisoftheL2-projectionandsomemixedfiniteelementprojections,weobtainthesuperconvergenceresultofleast-squaresmixedfiniteelementsolutions.ThiserrorestimateindicatesanaccuracyofO(h3/2)ifthelowestorderRaviart-Thomaselementsareemployed.

简介：Wedeveloptheinterpolatedfiniteelementmethodtosolvesecond-orderhy-perbolicequations.Thestandardlinearfiniteelementsolutionisusedtogenerateanewsolutionbyquadraticinterpolationoveradjacentelements.Weprovethatthisinterpo-latedfiniteelementsolutionhassuperconvergence.Thismethodcaneasilybeappliedtogeneratingmoreaccurategradienteitherlocallyorglobally,dependingontheapplications.Thismethodisalsocompletelyvectorizableandparallelizabletotaketheadvantagesofmoderncomputerstructures.Severalnumericalexamplesarepresentedtoconfirmourtheoreticalanalysis.

简介：ThemainaimofthispaperistostudytheapproximationtoviscoelasticitytypeequationswithaCrouzeix-Raviarttypenonconformingfiniteelementontheanisotropicmeshes.Thesuperclosepropertyoftheexactsolutionandtheoptimalerrorestimateofitsderivativewithrespecttotimearederivedbyusingsomenoveltechniques.Moreover,employingapostprocessingtechnique,theglobalsuperconvergencepropertyforthediscretizationerrorofthepostprocesseddiscretesolutiontothesolutionitselfisstudied.