Finite Element Techniques for Fluid Flow

112 INTERPOLATION FUNCTIONS

The matrix K can now be assembled, as

1

K

4A

ilKh

+

VJ

(g)

-Γ

Next, we form the P matrix which can be defined for q

n

acting

only on the 2-3 side (ξ

ι

= 0), as

0

ξ

2

(2ξ

2

- 1)

É3(2É3 - 1)

node 2 I 0

0

Let us assume q

n

is constant over that side for simplicity, though it

would not be difficult to consider the q

n

varying, for instance,

linearly, if necessary

;

i.e.

q

n

dS

(h)

In = Inl^l + <7n3£3

After integrating (h) using formula (3.20), we have

(i)

P =\

m»

(j)

(/ = length of the side.)

3.3 FIRST-ORDER CONTINUITY FUNCTIONS

FOR RECTANGULAR ELEMENTS

SYSTEM OF COORDINATES

For rectangular elements (Figure 3.6) we can define