Finite Element Techniques for Fluid Flow

66 THE FINITE ELEMENT TECHNIQUE

should have the terms giving zero derivatives [such as cc

i

+ a

2

x

for a functional with d

2

( )/dx

2

] and those that give constant de-

rivatives in the functional (such as

a

3

x

2

for the above case). In

general non-compatible models have to be carefully studied before

use,

for instance by taking into account the work due to the dis-

continuities and seeing if it becomes zero when the element size

tends to be infinitely small.

2.3 ELEMENT MATRICES

We will now deduce the properties of a single element. We have

already mentioned that the expansions for the element unknowns

can be written in terms of the nodal values of