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1、CSCI,MATH6860FINITEELEMENTANALYSISLectureNotes:Spring2000JosephE.FlahertyAmosEatonProfessorDepartmentofComputerScienceDepartmentofMathematicalSciencesRensselaerPolytechnicInstituteTroy,NewYork12180c2000,JosephE.Flaherty,allrightsreserved.Thesenotesareint

2、endedforclassroomusebyRensselaerstudentstakingcoursesCSCI,MATH6860.Copyingordownloadingbyothersforpersonaluseisacceptablewithnoticationoftheauthor.iiCSCI,MATH6860:FiniteElementAnalysisSpring2000Outline1.Introduction1.1.HistoricalPerspective1.2.WeightedR

3、esidualMethods1.3.ASimpleFiniteElementProblem2.One-DimensionalFiniteElementMethods2.1.Introduction2.2.Galerkin'sMethodandExtremalPrinciples2.3.EssentialandNaturalBoundaryConditions2.4.PiecewiseLagrangeApproximation2.5.HierarchicalBases2.6.InterpolationEr

4、rors3.Multi-DimensionalVariationalPrinciples3.1.Galerkin'sMethodandExtremalPrinciples3.2.FunctionSpacesandApproximation3.3.OverviewoftheFiniteElementMethod4.FiniteElementApproximation4.1.Introduction4.2.LagrangeBasesonTriangles4.3.LagrangeBasesonRectangl

5、es4.4.HierarchicalBases4.5.Three-dimensionalBases4.6.InterpolationErrors5.MeshGenerationandAssembly5.1.Introductioniii5.2.MeshGeneration5.3.DataStructures5.4.CoordinateTransformations5.5.GenerationofElementMatricesandTheirAssembly5.6.AssemblyofVectorSyst

6、ems6.NumericalIntegration6.1.Introduction6.2.One-DimensionalGaussianQuadrature6.3.Multi-DimensionalGaussianQuadrature7.DiscretizationErrors7.1.Introduction7.2.ConvergenceandOptimality7.3.Perturbations8.Adaptivity8.1.Introduction8.2.h-Renement8.3.p-andhp

7、-Renement9.ParabolicProblems9.1.Introduction9.2.Semi-DiscreteGalerkinMethods:TheMethodofLines9.3.FiniteElementMethodsinTime9.4.ConvergenceandStability9.5.Convection-DiusionSystems10.HyperbolicProblems10.1.Introduction10.2.FlowProblemsandUpwindWeighting

8、10.3.ArticialDiusioniv10.4.StreamlineWeighting11.LinearSystemsSolution11.1.Introduction11.2.BandedGaussianEliminationandProleTechniques11.3.NestedDissectionandDomainDecomposition11.4.ConjugateGradientMethods11.5.Nonline