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偏微分方程的数值近似法

偏微分方程的数值近似法

定 价:¥81.00

作 者: (意)Alfio Quarteroni,[意]Alberto Valli著
出版社: 世界图书出版公司北京公司
丛编项:
标 签: 微积分

ISBN: 9787506236171 出版时间: 1998-03-01 包装: 简裝本
开本: 20cm 页数: 543 字数:  

内容简介

  out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations.

作者简介

暂缺《偏微分方程的数值近似法》作者简介

图书目录

PartI.BasicConceptsandMethodsforPDEs'Approximation
1.Introduction
1.1TheConceptualPathBehindtheApproximation
1.2PreliminaryNotationandFunctionSpaces
1.3SomeResultsAboutSobolevSpaces
1.4ComparisonResults
2.NumericalSolutionofLinearSystems
2.1DirectMethods
2.1.1BandedSystems
2.1.2ErrorAnalysis
2.2GeneralitiesonIterativeMethods
2.3ClassicalIterativeMethods
2.3.1JacobiMethod
2.3.2Gauss:SeidelMethod
2.3.3RelaxationMethods(S.O.R.andS.S.O.R.)
2.3.4ChebyshevAccelerationMethod
2.3.5TheAlternatingDirectionIterativeMethod
2.4ModernIterativeMethods
2.4.1PreconditionedRichardsonMethod
2.4.2ConjugateGradientMethod
2.5Preconditioning
2.6ConjugateGradientandLanczoslikeMethodsfor
Non-SymmetricProblems
2.6.1GCR,OrthominandOrthodirIterations
2.6.2ArnoldiandGMRESIterations
2.6.3Bi-CG,CGSandBi-CGSTABIterations
2.7TheMulti-GridMethod
2.7.1TheMulti-GridCycles
2.7.2ASimpleExample
2.7.3Convergence
2.8Complements
3.FiniteElementApproximation
3.1Triangulation
3.2Piecewise-PolynomialSubspaces
3.2.1TheScalarCase
3.2.2TheVectorCase
3.3DegreesofFreedomandShapeFunctions
3.3.1TheScalarCase:TriangularFiniteElements
3.3.2TheScalarCase:ParallelepipedalFiniteElements
3.3.3TheVectorCase
3.4TheInterpolationOperator
3.4.1InterpolationError:theScalarCase
3.4.2InterpolationError:theVectorCase
3.5ProjectionOperators
3.6Complements
4.PolynomialApproximation
4.1OrthogonalPolynomials
4.2GaussianQuadratureandInterpolation
4.3ChebyshevExpansion
4.3.1ChebyshevPolynomials
4.3.2ChebyshevInterpolation
4.3.3ChebyshevProjections
4.4LegendreExpansion
4.4.1LegendrePolynomials
4.4.2LegendreInterpolation
4.4.3LegendreProjections
4.5Two-DimensionalExtensions
4.5.1TheChebyshevCase
4.5.2TheLegendreCase
4.6Complements
5.Galerkin,CollocationandOtherMethods
5.1AnAbstractReferenceBoundaryValueProblem
5.1.1SomeResultsofFunctionalAnalysis
5.2GalerkinMethod
5.3Petrov-GalerkinMethod
5.4CollocationMethod
5.5GeneralizedGalerkinMethod
5.6Time-AdvancingMethodsforTime-DependentProblems
5.6.1Semi-DiscreteApproximation
5.6.2Fully-DiscreteApproximation
5.7Fractional-StepandOperator-SplittingMethods
5.8Complements
PartII.ApproximationofBoundaryValueProblems
6.EllipticProblems:ApproximationbyGalerkinand
CollocationMethods
6.1ProblemFormulationandMathematicalProperties
6.1.1VariationalFormofBoundaryValueProblems
6.1.2Existence,UniquenessandA-PrioriEstimates
6.1.3RegularityofSolutions
6.1.4OntheDegeneracyoftheConstantsinStability
andErrorEstimates...
6.2NumericalMethods:ConstructionandAnalysis
6.2.1GalerkinMethod:FiniteElementandSpectral
Approximations
6.2.2SpectralCollocationMethod
6.2.3GeneralizedGalerkinMethod
6.3AlgorithmicAspects
6.3.1AlgebraicFormulation
6.3.2TheFiniteElementCase
6.3.3TheSpectralCollocationCase
6.4DomainDecompositionMethods
6.4.1TheSchwarzMethod
6.4.2Iteration-by-SubdomainMethodsBasedon
TransmissionConditionsattheInterface
6.4.3TheSteklov-PoincareOperator
6.4.4TheConnectionBetweenIterations-by-Subdomain
MethodsandtheSchurComplementSystem
7.EllipticProblems:ApproximationbyMixedand
HybridMethods
7.1AlternativeMathematicalFormulations
7.1.1TheMinimumComplementaryEnergyPrinciple
7.1.2Saddle-PointFormulations:MixedandHybrid
Methods
7.2ApproximationbyMixedMethods
7.2.1SettingupandAnalysis
7.2.2AnExample:theRaviart-ThomasFiniteElements
7.3SomeRemarksontheAlgorithmicAspects
2.4TheApproximationofMoreGeneralConstrained
Problems
7.4.1AbstractFormulation
7.4.2AnalysisofStabilityandConvergence
7.4.3HowtoVerifytheUniformCompatibilityCondition
7.5Complements
8.SteadyAdvection-DiffusionProblems
8.1MathematicalFormulation
8.2AOne-DimensionalExample
8.2.1GalerkinApproximationandCenteredFinite
Differences
8.2.2UpwindFiniteDifferencesandNumericalDiffusion
8.2.3SpectralApproximation
8.3StabilizationMethods
8.3.1TheArtificialDiffusionMethod
8.3.2StronglyConsistentStabilizationMethodsfor
FiniteElements
8.3.3StabilizationbyBubbleFunctions
8.3.4StabilizationMethodsforSpectralApproximation
8.4AnalysisofStronglyConsistentStabilizationMethods
8.5SomeNumericalResults
8.6TheHeterogeneousMethod
9.TheStokesProblem
9.1MathematicalFormulationandAnalysis
9.2GalerkinApproximation
9.2.1AlgebraicFormoftheStokesProblem
9.2.2CompatibilityConditionandSpuriousPressure
Modes
9.2.3Divergence-FreePropertyandLockingPhenomena
9.3FiniteElementApproximation
9.3.1DiscontinuousPressureFiniteElements
9.3.2ContinuousPressureFiniteElements
9:4StabilizationProcedures
9.5ApproximationbySpectralMethods
9.5.1SpectralGalerkinApproximation
9.5.2SpectralCollocationApproximation
9.5.3SpectralGeneralizedGalerkinApproximation
9.6SolvingtheStokesSystem
9.6.1ThePressure-MatrixMethod
9.6.2TheUzawaMethod
9.6.3TheArrow-HurwiczMethod
9.6.4PenaltyMethods
9.6.5TheAugmented-LagrangianMethod
9.6.6MethodsBasedonPressureSoIvers
9.6.7AGlobalPreconditioningTechnique
9.7Complements
10.TheSteadyNavier-StokesProblem
10.1MathematicalFormulation
10.1.1OtherKindofBoundaryConditions
10.1.2AnAbstractFormulation
10.2FiniteDimensionalApproximation
10.2.1AnAbstractApproximateProblem
10.2.2ApproximationbyMixedFiniteElementMethods
10.2.3ApproximationbySpectralCollocationMethods
10.3NumericalAlgorithms
10.3.1NewtonMethodsandtheContinuationMethod
10.3.2AnOperator-SplittingAlgorithm
10.4StreamFunction-VorticityFormulationofthe
Navier-StokesEquations
10.5Complements
PartIII.ApproximationofInitial-BoundaryValueProblems
11.ParabolicProblems
11.1Initial-BoundaryValueProblemsandWeakFormulation
11.1.1MathematicalAnalysisofInitial-BoundaryValue
Problems
11.2Semi-DiscreteApproximation
11.2.1TheFiniteElementCase
11.2.2TheCaseofSpectralMethods
11.3Time-AdvancingbyFiniteDifferences
11.3.1TheFiniteElementCase
11.3.2TheCaseofSpectralMethods
11.4SomeRemarksontheAlgorithmicAspects
11.5Complements
12.UnsteadyAdvection-DiffusionProblems
12.1MathematicalFormulation
12.2Time-AdvancingbyFiniteDifferences
12.2.1ASharpStabilityResultforthe0-scheme
12.2.2ASemi-ImplicitScheme
12.3TheDiscontinuousGalerkinMethodforStabilized
Problems
12.4Operator-SplittingMethods
12.5ACharacteristicGalerkinMethod
13.TheUnsteadyNavier-StokesProblem
13.1TheNavier-StokesEquationsforCompressibleand
IncompressibleFlows
13.1.1CompressibleFlows
13.1.2IncompressibleFlows
13.2MathematicalFormulationandBehaviourofSolutions
13.3Semi-DiscreteApproximation
13.4Time-AdvancingbyFiniteDifferences
13.5Operator-SplittingMethods
13.6OtherApproaches
13.7Complements
14.HyperbolicProblems
14.1SomeInstancesofHyperbolicEquations
14.1.1LinearScalarAdvectionEquations
14.1.2LinearHyperbolicSystems
14.1.3Initial-BoundaryValueProblems
14.1.4NonlinearScalarEquations
14.2ApproximationbyFiniteDifferences
14.2.1LinearScalarAdvectionEquationsandHyperbolic
Systems
14.2.2Stability,Consistency,Convergence
14.2.3NonlinearScalarEquations
14.2.4HighOrderShockCapturingSchemes
14.3ApproximationbyFiniteElements
14.3.1GalerkinMethod
14.3.2StabilizationoftheGalerkinMethod
14.3.3Space-DiscontinuousGalerkinMethod
14.3.4SchemesforTime-Discretization
14.4ApproximationbySpectralMethods
14.4.1SpectralCollocationMethod:theScalarCase
14.4.2SpectralCollocationMethod:theVectorCase
14.4.3Time-AdvancingandSmoothingProcedures
14.5SecondOrderLinearHyperbolicProblems
14.6TheFiniteVolumeMethod
14.7Complements
References
SubjectIndex

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