Theory and Practice of Finite Elements

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Springer Science & Business Media, 29.04.2004 - 526 Seiten
The origins of the finite element method can be traced back to the 1950s when engineers started to solve numerically structural mechanics problems in aeronautics. Since then, the field of applications has widened steadily and nowadays encompasses nonlinear solid mechanics, fluid/structure interactions, flows in industrial or geophysical settings, multicomponent reactive turbulent flows, mass transfer in porous media, viscoelastic flows in medical sciences, electromagnetism, wave scattering problems, and option pricing (to cite a few examples). Numerous commercial and academic codes based on the finite element method have been developed over the years. The method has been so successful to solve Partial Differential Equations (PDEs) that the term "Finite Element Method" nowadays refers not only to the mere interpolation technique it is, but also to a fuzzy set of PDEs and approximation techniques. The efficiency of the finite element method relies on two distinct ingredi ents: the interpolation capability of finite elements (referred to as the approx imability property in this book) and the ability of the user to approximate his model (mostly a set of PDEs) in a proper mathematical setting (thus guar anteeing continuity, stability, and consistency properties). Experience shows that failure to produce an approximate solution with an acceptable accuracy is almost invariably linked to departure from the mathematical foundations. Typical examples include non-physical oscillations, spurious modes, and lock ing effects. In most cases, a remedy can be designed if the mathematical framework is properly set up.
 

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Inhalt

I
3
III
19
IV
31
V
38
VI
58
VII
68
VIII
75
IX
77
XXXIX
300
XL
312
XLI
332
XLII
337
XLIV
340
XLV
346
XLVI
354
XLVII
357

X
81
XII
88
XIII
93
XIV
99
XV
106
XVI
111
XVIII
120
XIX
141
XX
150
XXI
164
XXII
170
XXIII
175
XXV
183
XXVI
201
XXVII
208
XXVIII
214
XXIX
219
XXXI
225
XXXII
234
XXXIII
242
XXXIV
251
XXXV
265
XXXVI
271
XXXVII
275
XXXVIII
279
XLVIII
368
XLIX
372
L
376
LI
380
LII
383
LIII
393
LIV
401
LV
413
LVI
417
LVII
421
LVIII
435
LIX
445
LX
453
LXI
457
LXII
463
LXIV
468
LXV
477
LXVI
480
LXVII
482
LXVIII
493
LXIX
497
LXX
513
LXXI
517
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