analyse num©rique et optimisation.[gr©goire.allaire]

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L'ouvrage complet est disponible auprs des ditions de l'cole Polytechnique Cliquez ici pour accder au site des ditions

LE CO

LY T PO

HN EC

UE IQ

OLE C

LY T PO

N CH E

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

H 1 () 1 H0 () H m () H(div) W m,p ()

OLE C

EC LY T PO

NIQ H

UE

C

LE O

LY T PO

HN EC

UE IQ

N = 1 P1 P2 N 2

PO LE CO

TEC LY

HN

OLE C

LY PO

CH TE

UE IQ

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

PO LE CO

TEC LY

HN

UE IQ

OLE C

EC LY T PO

NIQ H

UE

C

LE O

LY T PO

HN EC

UE IQ

PO LE CO

TEC LY

HN

UE IQ

C

OLE

LY PO

CH TE

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

OLE C

LY PO

CH TE

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

OLE C

LY PO

CH TE

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

OLE C

LY PO

CH TE

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

OLE C

LY PO

CH TE

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

C

LE O

LY T PO

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UE IQ

OLE C

LY PO

N C H TE

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

OLE C

LY PO

CH TE

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

C

LE O

LY T PO

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UE IQ

OLE C

LY PO

CH TE

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

C

U E H N I Q C

LE O

LY T PO

HN EC

UE IQ

C

OLE

YTE POL

C

LE O

LY T PO

HN EC

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

N RN N = 1, 2 x t f (x, t) (x, t) c c V

OLE C

LY PO

CH TE

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

d dt

PO LE CO

V V ds n V q q n ds =V V

TEC LYc dx =V V

HNV

UE IQ

f dx

q n ds

divq dx.

V + divq = f c t x t N qi divq = q = (q1 , ..., qN )t . xi i=1

k =

OLE C

LY PO

CH TE t

N

UE IQ

q = k,

.

, ..., x1 xN

c k = f, t

= div

=

C

LE O

LY T POi=1

N

2 . x2 i

HN EC

UE IQ

n

C

LE O

LY T PO

HN EC

UE IQ

t = 0 (t = 0, x) = 0 (x),

0

OLE C

LY T PO

N CH E

UE IQ

(t, x) = 0 x t > 0.

(t, x) n(x) (t, x) = 0 x t > 0, n

n

(t, x) + (t, x) = 0 x , t > 0 n

C

LE O

LY T PO

HN EC

UE IQ

c k = f (x, t) R+ t (x, t) R+ (t, x) = 0 (t = 0, x) = (x) x 0

C

LE O

LY T PO

HN EC

UE IQ

K c J/(kg K) k Jm2 /(kg K s) c k

D N F D , N , F

(f, 0 ) (f, 0 ) k q

OLE C

LY PO

CH TE

N

UE IQ

C

LE O

LY T PO

HN EC

UE IQ

q k c

C

LE O

LY T PO

HN EC

UE IQ

x u k T u 2u u ru + 1/2rx + 1/2 2 x2 2 = 0 (x, t) R (0, T ) t x x u(t = T, x) = max(x k, 0) x R

u(0, x) t = 0 k T > 0 x t = 0 r V (x, t) RN V c + cV k = f R+ t =0 R+ (t = 0, x) = (x) 0

OLE C

LY PO

CH TE

N

UE IQ

C

LE O

LY T POPe = cV L , k

HN EC

UE IQ

C

L c + cV = f R+ t (x, t) R+ V (x) n(x) < 0 (t, x) = 0 (t = 0, x) = (x) 0

LE O

LY T PO

HN EC

UE IQ

V = R f V 2 +V 2 = 0 (x, t) R R+ t x x (t = 0, x) = 0 (x) x R

OLE C = k/c

LY PO

CH TE

N

UE IQ

+

1 (t, x) = 4t

0 (y) exp

(x V t y)2 4t

dy.

V = 0

R

0

+V =0 (x, t) R R+ t x (t = 0, x) = (x) x R 0

C

LE O

LY T PO

HN EC

UE IQ

C

0 R

LE O

LY T PO

(t, x) = 0 (x V t)

HN EC

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