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Fig. 12.4
Condition number
for hat functions (
top
)and
wavelets with preconditioning
(
bottom
)
Consider the problem (
12.8
) where we drop the
for notational simplicity. For a
C
1
(J, V
L
)
with
w(T )
test function
w
0, we integrate the variational formulation
with respect to the time variable
t
and use integration by parts to obtain
∈
=
(∂
t
u
L
,w)
a(u
L
,w)
d
t
+
=
0
J
a(u
L
,w)
d
t
(u
L
,w
)
⇒
−
+
=
(u
L,
0
,w(
0
)).
J
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