er
f
s
Γ
n
TN
d
u˚
d
λ
Sf
Sf(df) = λf
S1
s
S1
s(λs) = ds
ds=df=dΓsur Γ×[0; T]
λs+λf= 0 sur Γ×[0; T]
Sf(dΓ) + Ss(dΓ) = 0 sur Γ×[0; T]
S1
s(−Sf(dΓ)) = dΓsur Γ×[0; T]
dNdΓλNλΓTN
G
G=S1
s◦ −Sf
TNTN+1
dN+1 =S1
s(−Sf(dN))
P
dN+1 =S1
s−SfdP
N+1
Tinit Tfin N0
t Tinit
TTinit
NN0
T < Tfin
dP
N+1 =P(dN,˚
dN,dN1, ...)
λN+1 =Sf(dP
N+1)
dN+1 =S1
s(λN+1)
NN+ 1 TT+ ∆t
P(dN,˚
dN,˚
dN1) = P(dN,uN,uN1) = dN+α0tuN+α1t(uNuN1)
α0= 1 α1= 0.5
dP
N+1 =dN+t
2(3uNuN1)
α0= 0 α1= 0 α0= 1 α1= 0
dN+1
dP
N+1
TNTN+1
λ
N=λN+λN+1
2
1 / 13 100%