Lectures on The Finite Element Method - Tata Institute of

145 Pages·2011·0.77 MB·English

Lectures on
The Finite Element Method
By
Ph. Ciarlet
TataInstituteofFundamentalResearch
Bombay
1975
Lectures on
The Finite Element Method
By
Ph. Ciarlet
Notesby
S. Kesavan,Akhil Ranjan
M. Vanninathan
TataInstituteofFundamentalResearch
Bombay
1975
(cid:13)c TataInstituteofFundamentalResearch,1975
No part of this book may be reproduced in any
formbyprint, microfilmoranyothermeanswith-
out written permission from the Tata Institute of
Fundamental Research, Colaba,Bombay400005
PrintedInIndia
By
AnilD.VedAtPrabhatPrinters, Bombay400004
AndPublished By
TheTataInstituteofFundamentalResearch, Bombay.

Acknowledgements
THE AUTHOREXPRESSEShis deep gratitude to Professor Ramana-
than for his very kind invitation to deliver these lectures at Bangalore,
aspartoftheT.I.F.R.–I.I.Sc. MathematicsProgramme. Also,theauthor
tankstheT.I.F.R.forfinancialsupport.
Ph. Ciarlet
v

Preface
OUR BASIC AIM has been to present some of the mathematical as-
pects of the finite element method, as well as some applications of the
finite element method for solving problems in Elasticity. This is why
important topics, such as curved boundaries, mixed and hybrid meth-
ods, time-dependent problems, etc..., are not covered here. No attempt
hasbeenmadetogiveanexhaustive bibliography.
vii

Contents
Acknowledgements v
Preface vii
1 TheAbstractProblem 1
2 Examples 9
3 TheFiniteElementMethodinitsSimplestForm 29
4 ExamplesofFiniteElements 35
5 GeneralPropertiesofFiniteElements 53
6 Interpolation TheoryinSobolevSpaces 59
7 ApplicationstoSecond-OrderProblems... 67
8 NumericalIntegration 77
9 TheObstacleProblem 95
10 ConformingFiniteElementMethodforthePlateProblem 103
11 Non-ConformingMethodsforthePlateProblem 113
ix