简介：Inthispaper,someeffectivecascadicmultigridmethodsareproposedforsolvingthelargescalesymmetricornonsymmetricalgebraicsystemsarisingfromthefinitevolumemethodsforsecondorderellipticproblems.Itisshownthatthesealgorithmsareoptimalinbothaccuracyandcomputationalcomplexity.Numericalexperimentsarereportedtosupportourtheory.

简介：Inthispaper,weconstructandanalyseamortarfinitevolumemethodforthediscretizationforthebiharmonicprobleminR2.Thismethodisbasedonthemortar-typeAdininonconformingfiniteelementspaces.TheoptimalorderH2-seminormerrorestimatebetweentheexactsolutionandthemortarAdinifinitevolumesolutionofthebiharmonicequationisestablished.

简介：在这份报纸，我们为一个semilinear问题扩大插入内推的系数的想法到三角形的有限体积元素方法。我们首先为semilinear的一个边界价值问题与插入内推的系数介绍三角形的有限体积元素方法椭圆形的方程。我们然后分别地在H1标准，L2标准和L鈭?标准导出集中估计。最后，一个例子被给说明建议方法的有效性。[从作者抽象]

简介：Inthispaper,finitevolumemethodonunstructuredmeshesisstudiedforaparabolicconvection-diffusionproblemonanopenboundedsetofR^d(d=2or3)withRobinboundarycondition.UpwindingapproximationsareadaptedtotreatboththeconvectiontermandRobinboundarycondition.Bydirectlygettingstartfromtheformulationofthefinitevolumescheme,numericalanalysisisdone.Byusingseveraldiscretefunctionalanalysistechniquessuchassummationbyparts,discretenorminequality,etal,thestabilityanderrorestimatesontheapproximatesolutionareestablished,existenceanduniquenessoftheapproximatesolutionandthe1stordertemporalnormandL^2andH^1spacialnormconvergencepropertiesareobtained.

简介：我们为Stokes方程在矩形的格子上构造一个新稳定的有限体积方法。最低相等顺序的一致有限元素对(piecewise双线性的速度和压力)并且为速度和压力的piecewise常数测试空格在这个方法被采用。我们显示出这个方法的稳定性并且在L2标准在H1标准和压力为速度证明集中的第一最佳的率。另外，第二命令为在L2标准的速度的最佳的错误估计被导出。说明理论结果的数字实验被包括。

简介：

简介：我们与弱Dirichlet边界条件为时间依赖者Hamilton-Jacobi方程学习数字方法。我们首先建议抽象单调近似计划的一个新班并且得到1/2的集中率。然后，根据摘要，集中结果，由最新构造单调内部和边界点上的有限体积近似，我们与弱Dirichlet边界条件为时间依赖者Hamilton-Jacobi方程获得会聚的有限体积计划。最后给一些数字结果。[从作者抽象]

简介：在这份报纸，我们讨论P的有限体积元素方法[1]-nonconforming为椭圆形的问题的四边的元素并且为一般四边的分区获得最佳的错误估计。一个最佳的cascadicmultigrid算法被建议解决nonsymmetric，大规模系统源于如此的discretization。数字实验被报导支持我们的理论结果。[从作者抽象]

简介：Anunstructuredmeshfinitevolumediscretisationmethodforsimulatingdiffusioninanisotropicmediaintwo-dimensionalspaceisdiscussed.Thistechniqueisconsideredasanextensionofthefullyimplicithybridcontrol-volumefinite-elementmethodanditretainsthelocalcontinuityofthefluxatthecontrolvolumefaces.Aleastsquaresfunctionrecon-structiontechniquetogetherwithanewfluxdecompositionstrategyisusedtoobtainanaccuratefluxapproximationatthecontrolvolumeface,ensuringthattheoverallaccuracyofthespatialdiscretisationmaintainssecondorder.Thispaperhighlightsthatthenewtechniquecoincideswiththetraditionalshapefunctiontechniquewhenthecorrectiontermisneglectedandthatitsignificantlyincreasestheaccuracyofthepreviouslinearschemeoncoarsemesheswhenappliedtomediathatexhibitverystrongtoextremeanisotropyratios.Itisconcludedthatthemethodcanbeusedonbothregularandirregularmeshes,andappearsindependentofthemeshquality.