Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

(a)
(b)
φ x 10 4
15
10
φ
1.00
0.95
0.90
0.85
1.00
5
0
– d2φ dφ
+ 200 = x 2
2 dx dx
0 < x < 1
φ = 0, x = 0, x = 1
– d2φ 60 dφ
+ = x 2
dx 2 x dx
1 < x < 2
φ = 1, x = 1
φ = 0. x = 2
The reader can easily verify that with this substituted into the original equation,
thus writing now in place of Eq. (2.11)
U d d
ÿ
dx dx …k ‡ kb† d
dx
The steady-state problem in one dimension 21
1 x
Exact
Optimal Petrov–Galerkin
Standard Galerkin
2.0 x
Fig. 2.5 Application of standard Galerkin and Petrov±Galerkin (optimal) approximation: (a) variable source
term equation with constants k and h; (b) variable source term with a variable U.
‡ Q ˆ 0 …2:29†
we obtain an identical expression to that of Eq. (2.24) providing Q is constant and a
standard Galerkin procedure is used.