Finite Element Techniques for Fluid Flow

18 WEIGHTED RESIDUAL AND VARIATIONAL METHODS

When the number of terms is infinite, we obtain the exact solution.

For the case a = b, the centre point (x = a/2, y = b/2) value is

a

2

_ _36·64/α\

2

)—

A

c

- u

exacl

- -^r-k

(8 + if + Â +

■

· O-4C = Wexact = ——h| C (m)

1.3 WEAK FORMULATIONS

The examples treated in the previous section were restricted to

self-adjoint operators and boundary conditions coinciding with the

essential boundary conditions. Weighted residual methods are

applicable for arbitrary operators and boundary conditions, and

we will discuss in this section a general procedure for formulating

weighted residual statements which allow