FINITE ELEMENT METHOD AND ANALYSIS FOR CHEMICAL-FLOODING SIMULATION

1.IntroductionThisarticlediscussestheenhanced0ilrecoverynumericalsimulationofthechemicalflood-ing(suchassurfactats,alcohol,polymers)c0mposed0f3-dimensional,multicomponent,muLtiphaseandincompressiblemixedfluids.Aftertheoilfieldiswaterfi0oded,thereisstillalargeamountofcrudeoilleftintheoildeposit.Thisamountofoil,boundedbycapillarypressure,cannotflow;or)asaresultofthedisadvantageousrateofflowbetweenthedisplacinganddisplacedphases,thevolumethattheinjectionfiowaffectsistoosmalltodrivethecrudeoil.By…     

HIGH-ACCURACY FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEM

1 IntroductionOptimal design or control is playing an increasingly importal role in engineering designwork. Efficient numerical methods are among the keys to successful application of optimalcontrol in practical work. With its wide range of application in scielltific and engineeringnumerical simulation, finite element approximation of optimal control problems plays a veryimportant role in numerical method of these problems. There have been eXtensive studies inthis respect, see, for example, […     

HIGHLY NONCONFORMING FINITE ELEMENT APPROXIMATIONS FOR A FOURTH ORDERVARIATIONAL INEQUALITY WITH CURVATURE OBSTACLE

The purpose of this paper is to obtain the optimal error estimates of O(h) for the highly nonconforming elements to a fourth order variational inequality with curvature obstacle in a convex domain with simply supported boundary by using the novel function splitting method and the orthogonal properties of the nonconforming finite element spaces.Morley‘s element approximation is our special case.     

SUPERCONVERGENCE OF THE MORTAR FINITE ELEMENT APPROXIMATION TO A PARABOLIC PROBLEM

1.IntroductionDomaindecompositionapproachesaremostimportanttechniqllesforsolvingpartialdifferentialequations.Suchreformulationsareusuallymotivatedbytheneedtocreatesolverswhichareeasilyparallelised,see[1]and[2].MostapplicationsusediscretizationsgridswhicharedeAnedgloballyoverthewholedomainandthensplitilltosubdomains.Inmechanics,.thisresultsinanoverallconformingapprotimatiollofthevelocityfield.However,itmightbemoreconvethelltandefficienttouseapproximationswhicharedefinedindependelltlyoneachsubd…     

GLOBAL SUPERCONVERGENCE FOR A MIXED FINITE ELEMENT METHOD FOR THE WAVE EQUATION

1.IntroductionWeconsiderthesecondorderhyperbolicequationwithinitialconditionswhereaCRZisaboundeddomainwithboundariesparalleltotheaxes.Forconvenience,weassumehomogeneousDirichletboundaryconditions'Weassumethatthefunctionsailandfareuniformlyboundedandmeasurable,andthespatialoperatorisuniformlyellipticinthesensethatthereexistpositiveconstantsorandPsuchthatInamixedfiniteelementformulationbothdisplacementsandstressesareapproximatedsimultaneously.ThispropertyisimportantincomputingDarcyvelocitieso…     

CHARACTERISTIC ALTERNATING-DIRECTION FINITE ELEMENT METHODS FOR NONRECTANGULAR REGIONS FOR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA AND ITS ANALYSIS

For coupled system of multilayer dynamics of fluids in porous media, the characteristic alternating-direction finite element methods for nourectangular regions applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, isoparametric transformation, patch approximation, operator-splitting, characteristic method, negative norm estimate, energy method, the theory of prior estimates and techniques are used. For the nourectangular regions case, optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved. These methods have been successfully used in multilayer oil resources migration-accumulation numerical simulation.     

GALERKIN ALTERNATING-DIRECTION METHODS FOR NONRECTANGULAR REGIONS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

For the transient behavior of a semiconductor device, the modified method of characteristics with alternating-direction finite element procedures for nonrectangular region is put forward. Some techniques, such as calculus of variations, isoparametric transformation, patch approximation, operator-splitting, characteristic method, symmetrical reflection, energy method, negative norm estimate and a prior estimates and techniques, are employed. In the nonrectangular region case, optimal order estimates in L2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved.     

CHARACTERISTIC FINITE DIFFERENCE METHODS FOR POSITIVE SEMIDEFINITE PROBLEM OF TWO-PHASE (OIL AND WATER)MISCIBLE FLOW IN POROUS MEDIA

Numericalsimulationoftwo-phase(oilandwater)miscibleflowinporousmediaisthe'mathematicalfoundationinenergyproblems.Forapositivedefiniteproblem,thefamousmathematicianandinitiatorofnumericalsimulationofoildeposit,J.Douglas,Jr.putforwardthefamouscharacteristicfinitedifferencemethodll'2].However,fornumericalanalysistherearoseseriousdifficulties.Heonlystudiedtheperiodiccasesandcoercivelysupposedthedictionmatrixoftheconcentrationequationispositivedefinite.Butinmanypracticalsituationsthediffusionmatr…