
150 Meshless methods and their numerical properties
norm of derivative reduces as the eld nodes are increased. Therefore, the
complete or Sobolev error norm is computed as
Eff
I
e
I
n
I
N
r
(),Sobolev normofthe orde
0
2
1
∑
()
=−
=
(4.12)
EE
f
x
f
x
j
I
e
j
I
n
Ij
N
r
() ,Sobolev normofthe orde
1
0
2
1, 1
,3
∑
()
=+
∂
∂
−
∂
∂
==
(4.13)
where (E)
0
and (E)
1
are the Sobolev error norms of the zeroth and rst-
order, respectively, and e and n are the exact and numerical values, respec-
tively. It is seen from Equation (4.13) that as the square of error in the values
of function and derivative is added at each eld node, the contribution of
the term (E)
0
to the ter ...