简介：Inthispaperweconsideranon-standardinverseheatconductionproblemfordeterminingsurfaceheatfluxfromaninteriorobservationwhichappearsinsomeappliedsubjects.Thisproblemisill-posedinthesensethatthesolution(ifitexists)doesnotdependcontinuouslyonthedata.AFouriermethodisappliedtoformulatearegularizedapproximationsolution,andsomesharperrorestimatesarealsogiven.

简介：在这份报纸，我们为本地不连续的Galerkin(LDG)学习错误的superconvergence为一个维的线性寓言的方程的有限元素方法当轮流出现的流动被使用时。我们证明如果我们使用piecewisek-th度多项式，在LDG答案和准确答案之间的错误是(k+2)在Radau的-th顺序superconvergent与合适的起始的discretization指。而且，我们也证明LDG答案是(k+2)为到准确答案的特别设计的错误的-th顺序superconvergent。尽管我们仅仅考虑周期的边界状况，这个边界条件不是必要的，自从我们不使用Fourier分析。我们的分析为任意的常规网孔并且为有任意的k的Pk多项式是有效的1。我们执行数字实验证明superconvergence率在这证明纸是锋利的。[从作者抽象]

简介：Inthiswork,systemofparabolicequationswithdiscontinuouscoefficientsisstudied.Thedomaindecompositionmethodmodifiedbyacharacteristicfiniteelementprocedureisapplied.Afunctionisdefinedtoapproximatethefluxesoninnerboundariesbyusingthesolutionatthepreviouslevel.Thustheparallelismisachieved.Convergenceanalysisanderrorestimatearealsopresented.

简介：Theproblemofconstructingamodelreferenceadaptivecontrollawforanuncertain1-dimensionalparabolicsystemisconsideredinthisarticle.Thecontrollerdesignedhereinvolvesonlytheplantstatebutnoitsderivatives.Aprioriboundsontheplant'suncertainparametersareusedtoproposeswitchinglawswhichserveasanadaptivemechanism.Theexponentialdecaytozeroofthestateerrorwithanyprescribedrateisguaranteedbychoosingacontrollerparametercorrespondingly.Numericalstudiesarealsopresentedtoillustratetheapplicabilityofthecontrollaw.

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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：Inthispaper,westudythesemi-discretemortarupwindfinitevolumeelementmethodwiththeCrouzeix-Raviartelementfortheparabolicconvectiondiffusionproblems.Itisprovedthatthesemi-discretemortarupwindfinitevolumeelementapproximationsderivedareconvergentintheH~1-andL~2-norms.

简介：TheembeddedboundarymethodforsolvingellipticandparabolicproblemsingeometricallycomplexdomainsusingCartesianmeshesbyJohansenandColella(1998,J.Comput.Phys.147,60)hasbeenextendedforellipticandparabolicproblemswithinteriorboundariesorinterfacesofdiscontinuitiesofmaterialpropertiesorsolutions.Secondorderaccuracyisachievedinspaceandtimeforbothstationaryandmovinginterfaceproblems.Themethodisconservativeforellipticandparabolicproblemswithfixedinterfaces.Basedonthismethod,afronttrackingalgorithmfortheStefanproblemhasbeendeveloped.Theaccuracyofthemethodismeasuredthroughcomparisonwithexactsolutiontoatwo-dimensionalStefanproblem.Thealgorithmhasbeenusedforthestudyofmeltingandsolidificationproblems.

简介：Inthispaperanelliptic-paraboliccoupledsystemarisingfromthefluid-solute-heatflowthroughasaturatedporousmediumisconsiderd.Theuniquenessandtheexistenceofclassicalsolutionsareproved.Theasymptoticbehaviorofsolutionsforlargetimeisshown,too.

简介：在这篇论文，我们与非线性的边界条件调查强烈联合的非线性的抛物线的系统的积极解决方案:[图形]在函数上的适当假设下面一，b，g，h，d和f，我们获得解决方案可以全球性存在或由利用上面、更低的解决方案技术在有限时间骤起。

简介：AhighlyefficientH1-Galerkinmixedfiniteelementmethod(MFEM)ispresentedwithlineartriangularelementfortheparabolicintegro-differentialequation.Firstly,somenewresultsabouttheintegralestimationandasymptoticexpansionsarestudied.Then,thesuperconvergenceoforderO(h2)forboththeoriginalvariableuinH1(π)normandthefluxp=uinH(div,π)normisderivedthroughtheinterpolationpostprocessingtechnique.Furthermore,withthehelpoftheasymptoticexpansionsandasuitableauxiliaryproblem,theextrapolationsolutionswithaccuracyO(h3)areobtainedfortheabovetwovariables.Finally,somenumericalresultsareprovidedtoconfirmvalidityofthetheoreticalanalysisandexcellentperformanceoftheproposedmethod.

简介：这份报纸涉及为一个维的充分非线性的秒顺序开发精确、有效的数字方法椭圆形、寓言的部分微分方程(PDE)。在纸我们在场为构造高顺序内部惩罚的一个一般框架为这些充分非线性的PDE的接近的粘性答案的不连续的Galerkin(IP-DG)方法。为了捕获解决方案的第二顺序衍生物uxx的断绝，u，三独立函数p1，p2和p3被介绍用各种各样的片面限制代表数字衍生物。建议DG框架，基于内在的PDE的非标准的混合明确的表达，把一个非线性的问题嵌进非线性被修改了包括第二顺序衍生物uxx的多重价值的方程的一个主要线性的系统。建议框架扩大有限差别框架由作者开发了在的一个同伴[9]并且允许用高顺序多项式和不一致的网孔的充分非线性的PDE的近似。除了非标准的混合明确的表达设置，另一个主要想法是由与微分操作符一致并且满足某些monotonicity(叫的g-monotonicity)的一个数字操作符代替充分非线性的微分操作符性质。保证如此的g-monotonicity，构造的关键是介绍数字时刻，它在建议DG框架起一个关键作用。g-monotonicity给DG方法能力选择算术地“改正”答案(即，粘性答案)在所有可能的答案之中。而且，g-monotonicity允许更有效的非线性的解答者的可能的发展能作为代数学的系统的特殊非线性被探索到decouple方程。这份报纸也为习惯于guage的几个数字测试问题论述并且分析数字结果建议DG方法的精确性和效率。[从作者抽象]

简介：Theoreticalanalysisoftheelectromagneticfielddistributioninthefocalregionofalongmetallicparabolicreflectorthathasitssurfacecoveredwithamagnetizedplasmalayerisderived.Theincidentwaveisconsideredtobewithageneralobliqueincidenceforbothparallelandperpendicularpolarizations.TheelectromagneticfieldintensityexpressionsalongthefocalregionareobtainedaccuratelyusingMaslov’smethod.Theeffectsofplasmathicknessonthereflectedandtransmittedfielddistributionsareinvestigated.Theeffectsofotherphysicalparameterssuchastheangleofincidenceandtheplasmaandcyclotronfrequenciesonthetransmittedfieldintensitydistributionalongthefocalregionarealsostudied.TheresultsobtainedbyMaslov’smethodandKirchhoff’sapproximationarefoundtobeinagoodagreement.