Finite Element Techniques for Fluid Flow

THE FINITE ELEMENT TECHNIQUE 81

(b) SECOND CASE (JT - XJi= 0)

Let

us

now study

the

case

for

which

^ = 0.

Thus

(JT

-

XJi)W

= 0

(2.50)

The problem reduces

to

determining the values

of λ

for which (2.50)

has non-trivial solutions. These values are obtained from

JT -kJt = 0

(2.51)

which gives

us a

series

of λ

{

values

or

eigenvalues. Each

of

these

values

is

associated with

a ^,

eigenvector.

The matrix M in (2.51)

is

positive definite,

but JT is

singular

due

to the zero-derivative type terms. We may impose some full restraint

conditions

in

order

to

make JT non-singular.

For

this case

we

will

eliminate

the

rows and columns corresponding

to

these unknowns ...