Finite Element Techniques for Fluid Flow

WEIGHTED RESIDUAL AND VARIATIONAL METHODS 7

Considering (b), we can write

for u satisfying homogeneous boundary conditions. If a

l9

a

3

are > 0

and a

3

< 0 in the interval 0 < x < 1, the operator is obviously

positive definite.

(iii) Operating on

yields

(a)

(b)

The operator is not self-adjoint due to the presence of the first

derivative term. Odd-order derivatives will lead to skew-symmetric

terms in J^* and G*. The essential boundary condition

is u

prescribed.

In this case, we take the nonessential (natural) boundary condition

as du/dx prescribed.

1.2 WEIGHTED RESIDUAL METHODS

Weighted residual methods are numerical procedures for approxi-

matin ...