Finite Element Techniques for Fluid Flow

INTERPOLATION FUNCTIONS 139

we remove this restriction and include the three second derivatives

as nodal quantities for the corner nodes. The six conditions on u

are u,

du/dS,

and

d

2

u/dS

2

at the ends. At this point, we have six

quantities per corner node and a total of 18 displacements. We can

introduce three additional quantities. Now, the normal slope is

quartic and requires

five

conditions. We already have u

n

and u

ns

at

the ends. The additional conditions must involve u

n

at an interior

point on the

side,

say, at the mid-point. There

are 21

unknowns

in

all

and we see

that

a

quintic polynomial

is

suitable.

The

nodal quantities

are summarise ...