教学经典教材：有限元（第3版）

图书标准信息

• 作者 [德]布拉文斯（Braess D.） 著
• 出版社 世界图书出版公司
• 出版时间 2012-03
• 版次 3
• ISBN 9787510042850
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 365页
• 正文语种 英语

【内容简介】

Thisdefinitiveintroductiontofiniteelementmethodshasbeenthoroughlyupdatedforthisthirdedition，whichfeaturesimportantnewmaterialforbothresearchandapplicationofthefiniteelementmethod.
Thediscussionofsaddlepointproblemsisalughlightofthebookandhasbeenelaboratedtoincludemanymorenonstandardapplications.Thechapteronapplicationsinelasticitynowcontainsacompletediscussionoflockingphenomena.
Thenumericalsolutionofellipticpartialdifferentialequationsisanimportantapplicationoffiniteelementsandtheauthordiscussesthissubjectcomprehensively.TheseequationsaretreatedasvariationalproblemsforwhichtheSobolevspacesaretherightframework.Graduatestudentswhodonotnecessarilyhaveanyparticularbackgroundindifferentialequationsbutrequireanintroductiontofiniteelementmethodswillfindthistextinvaluable.Specifically，thechapteronfiniteelementsinsolidmechanicsprovidesabridgebetweenmathematicsandengineering.

【目录】

PrefacetotheThirdEnglishEdition
PrefacetotheFirstEnglishEdition
PrefacetotheGermanEdition
Notation
ChapterⅠIntroduction
1.ExamplesandClassificationofPDE's
Examples
ClassificationofPDE's
Well-posedproblems
Problems
2.TheMaximumPtinciple
Examples
Corollaries
Problem
3.FiniteDifferenceMethods
Discretization
Discretemaximumprinciple
Problem
4.AConvergenceTheoryforDifferenceMethods
Consistency
Localandglobalerror
Limitsofthecon-vergencetheory
Ptoblems

ChapterⅡConformingFiniteElements
1.SobolevSpaces
IntroductiontoSobolevspaces
Friedrichs'inequality
PossiblesingularitiesofH1functions
Compactimbeddings
Problems
2.VariationalFormulationofEllipticBoundary-ValueProblemsofSecondOrder
Variationalformulation
Reductiontohomogeneousbound-aryconditions
Existenceofsolutions
Inhomogeneousboundaryconditions
Problems
3.TheNeumannBoundary-ValueProblem.ATraceTheorem
EllipticityinH
Boundary-valueproblemswithnaturalbound-aryconditions
Neumannboundaryconditions
Mixedboundaryconditions
Proofofthetracetheorem
Practi-calconsequencesofthetracetheorem
Problems
4.TheRitz-GalerkinMethodandSomeFiniteElements
Modelproblem
Problems
5.SomeStandardFiniteElements
Requirementsonthemeshes
Significanceofthedifferentia-bilityproperties
Triangularelementswithcompletepolyno-mials
RemarksonClelements
Bilinearelements
Quadraticrectangularelements
Affinefamilies
Choiceofanelement
Problems
6.ApproximationProperties
TheBramble-Hilbertlemma
Triangularelementswithcom-pletepolynomials
Bilinearquadrilateralelements
In-verseestimates
Clement'sinterpolation
Appendix:Ontheoptimalityoftheestimates
Problems
7.ErrorBoundsforEllipticProblemsofSecondOrder
Remarksonregularity
ErrorboundsintheenergynormL2estimates
AsimpleLooestimate
TheL2-projector
Problems
8.ComputationalConsiderations
Assemblingthestiffnessmatrix
Staticcondensation
Complexityofsettingupthematrix
Effectonthechoiceofagrid
Localmeshrefinement
ImplementationoftheNeumannboundary-valueproblem
Problems

ChapterⅢNonconformingandOtherMethods
1.AbstractLemmasandaSimpleBoundaryApproximationGeneralizationsofCea'slemma
Dualitymethods
TheCrouzeix-Raviartelement
Asimpleapproximationtocurvedboundaries
Modificationsofthedualityargument
Problems
2.IsoparametricElements
Isoparametrictriangularelements
Isoparametricquadrilateralelements
Problems
3.FurtherToolsfromFunctionalAnalysis
Negativenorms
Adjointoperators
Anabstractexis-tencetheorem
Anabstractconvergencetheorem
ProofofTheorem3.4
Problems
4.SaddlePointProblems
Saddlepointsandminima
Theinf-supcondition
Mixedfiniteelementmethods
Fortininterpolation
……
ChapterⅣTheConjugateGradientMethod
ChapterⅤMultigridMethods
ChapterⅥFiniteElementsinSolidMechanics