Finite Element Techniques for Fluid Flow

126 INTERPOLATION FUNCTIONS

The derivatives (h) can now be expressed as

du

δχ

du

Ty

1= Bu"

(j)

The variational statement corresponding to Laplace's equation is

CC I, dudèu , dudèu\

J J

f

c Jo

If we define

an

element property matrix,

we can

express

the

left-hand

side

of

(k)

as

where

ôu

n

>

T

f f

B

T

HB(abs. value |J|) d£ drçu"

(1)

Jo

Jo

■ Ί

hj

To find the corresponding P matrix we need to integrate the right-

hand side of (k) on, for instance, side 2-3. q

n

is the constant flux

normal to the boundary, / is the length. Hence

j

q

H

ôudS

= ôu'-

T

qjj

0

n

(l-i,)

0

\ άη = ôu"-

T

q„l\

fol

1

1

i

2

OJ

(m)

In general we have

dS =

and

f*(tr

dS =

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