有限元方法的数学理论（第3版）

图书标准信息

• 作者 布雷（Brenner S.C.） 著
• 出版社 世界图书出版公司
• 出版时间 2010-09
• 版次 3
• ISBN 9787510027437
• 定价 55.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 397页
• 正文语种 英语

【内容简介】

Thiseditioncontainsfournewsectionsonthefollowingtopics：theBDDCdomaindecompositionpreconditioner（Section7.8）,aconvergentadaptivealgorithm（Section9.5）,interiorpenaltymethods（Section10.5）andPoincare-FriedrichsinequalitiesforpiecewiseWp1functions（Section10.6）.Wehavemadeimprovementsthroughoutthetext,manyofwhichweresuggestedbycolleagues,towhomwearegrateful.Newexerciseshavebeenaddedandthelistofreferenceshasalsobeenexpandedandupdated.

【目录】

seriespreface
prefacetothethirdedition
prefacetothesecondedition
prefacetothefirstedition
0basicconcepts
0.1weakformulationofboundaryvalueproblems
0.2ritz-galerkinapproximation
0.3errorestimates
0.4piecewisepolynomialspaces-thefiniteelementmethod
0.5relationshiptodifferencemethods
0.6computerimplementationoffiniteelementmethods
0.7localestimates
0.8adaptiveapproximation
0.9weightednormestimates
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
3.3theinterpolant
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
4.9adiscretesobolevinequality
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

6finiteelementmultigridmethods
6.1amodelproblem
6.2mesh-dependentnorms
6.3themultigridalgorithm
6.4approximationproperty
6.5w-cycleconvergenceforthekthleveliteration
6.6]/-cycleconvergenceforthekthleveliteration
6.7fullmultigridconvergenceanalysisandworkestimates
6.xexercises

7additiveschwarzpreconditioners
7.1abstractadditiveschwarzframework
7.2thehierarchicalbasispreconditioner
7.3thebpxpreconditioner
7.4thetwo-leveladditiveschwarzpreconditioner
7.5nonoverlappingdomaindecompositionmethods
7.6thebpspreconditioner
7.7theneumann-neumannpreconditioner
7.8thebddcpreconditioner
7.xexercises

8max-normestimates
8.1maintheorem
8.2reductiontoweightedestimates
8.3proofoflemma8.2.6
8.4proofsoflemmas8.3.7and8.3.11
8.5lpestimates（regularcoefficients）
8.6lpestimates（irregularcoefficients）
8.7anonlinearexample
8.xexercises

9adaptivemeshes
9.1aprioriestimates
9.2errorestimators
9.3localerrorestimates
9.4estimatorsforlinearformsandothernorms
9.5aconvergentadaptivealgorithm
9.6conditioningoffiniteelementequations
9.7boundsontheconditionnumber
9.8applicationstotheconjugate-gradientmethod
9.xexercises

10variationalcrimes
10.1departurefromtheframework
10.2finiteelementswithinterpolatedboundaryconditions
10.3nonconformingfiniteelements
10.4isoparametricfiniteelements
10.5discontinuousfiniteelements
10.6poincare-friedrichsinequalititesforpiecewisew1pfunctions
10.xexercises

11applicationstoplanarelasticity
11.1theboundaryvalueproblems
11.2weakformulationandkorn'sinequality
11.3finiteelementapproximationandlocking
11.4arobustmethodforthepuredisplacementproblem
11.xexercises

12mixedmethods
12.1examplesofmixedvariationalformulations
12.2abstractmixedformulation
12.3discretemixedformulation
12.4convergenceresultsforvelocityapproximation
12.5thediscreteinf-supcondition
12.6verificationoftheinf-supcondition
12.xexercises

13iterativetechniquesformixedmethods
13.1iteratedpenaltymethod
13.2stoppingcriteria
13.3augmentedlagrangianmethod
13.4applicationtothenavier-stokesequations
13.5computationalexamples
13.xexercises

14applicationsofoperator-interpolationtheory
14.1therealmethodofinterpolation
14.2realinterpolationofsobolevspaces
14.3finiteelementconvergenceestimates
14.4thesimultaneousapproximationtheorem
14.5precisecharacterizationsofregularity
14.xexercises
references
index