Annexesmathématiques
288
∇ ⋅ = ∇ 




 + ∇ ∧
(
) ∧
u u
u
u
u
2
2
 = ∇ + ∇
( )
(
)
1
2
u
u
t
Ω = ∇ − ∇
( )
(
)
1
2
u
u
t


∇ = +
u
 Ω
∇ ⋅ = ∇
( )
u
u
tr
∇ ⋅ ( ) = ∇ ⋅
(
)
Δ
Δ
u
u
∇ ⋅ (
) =
∇ ∧
u
0
∇ ⋅ ( ) = ∇ ⋅ + ∇
⋅
 
 
f u
u u
f
f
∇ ⋅ ( ) = ∇ ⋅ + ⋅ ∇
 
 
f A
f
A A
f
∇ ⋅ ( ) = ∇
f I
f
∇ ⋅ ∧
(
) = ⋅ ∇ ∧ − ⋅ ∇ ∧
u v
v
u u
v
 ∇ ⋅ ⊗
(
) = ∇ ⋅ + ∇ ⋅
u v
u
v
u v
∇
=
+ ∇ ∧ ∇ ∧
(
) = ∇ ∇
(
) +
⋅
⋅
 Δ
Δ
u
u
u
u
1
2
1
2
1
2
∇ ⋅ = ∇ ∧ ∇ ∧
(
)
Ω
1
2
u
Δf
f
= ∇ ⋅ ∇
( )
Δu
u
u
u
= ∇ ⋅ ∇
( ) = ∇ ∇
( ) − ∇ ∧ ∇ ∧
(
)
.
Δ
Δ
Δ
f g
f g g f
f
g
( ) =
+
+ ∇ ⋅ ∇
2
Δ
Δ
Δ
f u
f u u f
f
u
( ) =
+
+ ∇ ⋅ ∇
2
∇ ∧ ∇
( ) =
f
0
∇ ∧ ( ) = ∇ ∧
(
)
  Δ
Δ
u
u
∇ ∧ ( ) = ⋅ ∇ ∧ + ∇ ∧
f u
f
u
f u
∇ ∧ ∧
(
) = ∇ ⋅ − ∇ ⋅ + ∇ ⋅ − ∇ ⋅
u v
u
v v
u
u v
v u
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