有限元方法中的数学理论 英文版
作者：（美）Susanne C.Brenner，（美）L.Ridgway Scott 著
出版时间： 1998年版
内容简介
Mathematics is playing an ever more important role in the physical and biological sciences， provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest， both in research and teaching， has led to the establishment of the series： Texts in Applied Mathematics （TAM）. The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques， such as numerical and symbolic computer systems， dynamical systems， and chaos，mix with and reinforce the traditional methods of applied mathematics. Thus. the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses， and will complement the Applied Math- ematical Sciences （AMS） series， which will focus on advanced textbooks and research level monographs.本书文英文版。
目录
Preface
0BasicConcepts
0.1WeakFormulationofBoundaryValueProblems
0.2Ritz-GalerkinApproximation
0.3ErrorEstimates
0.4PiecewisePolynomialSpaces-TheFiniteElementMethod
0.5RelationshiptoDifferenceMethods
0.6ComputerImplementationofFiniteElementMethods
0.7LocalEstimates
0.8WeightedNormEstimates
0.xExercises
1SobolevSpaces
1.1ReviewofLebesgueIntegrationTheory
1.2Generalized(weak)Derivatives
1.3SobolevNormsandAssociatedSpaces
1.4InclusionRelationsandSobolev'sInequality
1.5ReviewofChapter0
1.6TraceTheorems
1.7NegativeNormsandDuality
1.xExercises
2VariationalFormulationofEllipticBoundaryValueProblems
2.1Inner-ProductSpaces
2.2HilbertSpaces
2.3ProjectionsontoSubspaces
2.4RieszRepresentationTheorem
2.5FormulationofSymmetricVariationalProblems
2.6FormulationofNonsymmetricVariationalProblems
2.7TheLax-MilgramTheorem
2.8EstimatesforGeneralFiniteElementApproximation
2.9Higher-dimensionalExamples
2.xExercises
3TheConstructionofaFiniteElementSpace
3.1TheFiniteElement
3.2TriangularFiniteElements
TheLagrangeElement
TheHermiteElement
TheArgyrisElement
3.3TileInterpolant
3.4EquivalenceofElements
3.5RectangularElements
TensorProductElements
TheSerendipityElement
3.6Higher-dimensionalElements
3.7ExoticElements
3.xExercises
4PolynomialApproximationTheoryinSobolevSpaces
4.1AveragedTaylorPolynomials
4.2ErrorRepresentation
4.3BoundsforRieszPotentials
4.4BoundsfortheInterpolationError
4.5InverseEstimates
4.6Tensor-productPolynomialApproximation
4.7IsoparametricPolynomialApproximation
4.8InterpolationofNon-smoothFunctions
4.xExercises
5n-DimensionalVariationalProblems
5.1VariationalFormulationofPoisson'sEquation
5.2VariationalFormulationofthePureNeumannProblem
5.3CoercivityoftheVariationalProblem
5.4VariationalApproximationofPoisson'sEquation
5.5EllipticRegularityEstimates
5.6GeneralSecond-OrderEllipticOperators
5.7VariationalApproximationofGeneralEllipticProblems
5.8Negative-NormEstimates
5.9ThePlate-BendingBiharmonicProblem
5.xExercises
FiniteElementMultigridMethods
6.1AModelProblem
6.2Mesh-DependentNorms
6.3TheMultigridAlgorithm
6.4ApproximationProperty
6.5W-cycleConvergenceforthekthLevelIteration
6.6v-cycleConvergenceforthekthLevelIteration
6.7FullMultigridConvergenceAnalysisandWorkEstimates
6.xExercises
Max-normEstimates
7.1MainTheorem
7.2ReductiontoWeightedEstimates
7.3ProofofLemma7.2.6
7.4ProofofLemmas7.3.7and7.3.11
7.5LpEstimates(RegularCoefficients)
7.6LpEstimates(IrregularCoefficients)
7.7ANonlinearExample
7.xExercises
VariationalCrimes
8.1DeparturefromtheFramework
8.2FiniteElementswithInterpolatedBoundaryConditions
8.3NonconformingFiniteElements
8.4IsoparametricFiniteElements
8.xExercises
9ApplicationstoPlanarElasticity
9.1TheBoundaryValueProblems
9.2WeakFormulationandKorn'sInequality
9.3FiniteElementApproximationandLocking
9.4ARobustMethodforthePureDisplacementProblem
9.xExercises
10MixedMethods
10.1ExamplesofMixedVariationalFormulations
10.2AbstractMixedFormulation
10.3DiscreteMixedFormulation
10.4ConvergenceResultsforVelocityApproximation
10.5TheDiscreteInf-SupCondition
10.6VerificationoftheInf-SupCondition
10.xExercises
11IterativeTechniquesforMixedMethods
11.1IteratedPenaltyMethod
11.2StoppingCriteria
11.3AugmentedLagrangianMethod
11.4ApplicationtotheNavier-StokesEquations
11.5ComputationalExamples
11.xExercises
12ApplicationsofOperator-InterpolationTheory
12.1TheRealMethodofInterpolation
12.2RealInterpolationofSobolevSpaces
12.3FiniteElementConvergenceEstimates
12.4TheSimultaneousApproximationTheorem
12.5PreciseCharacterizationsofRegularity
12.xExercises
References
Index
