
Formulation of classical meshless methods 15
the FEM. The local nature of the function approximation is preserved as
the WF
vanishes beyond certain distance. The stationarity of J with
respect to
leads to
ux NxuNxPxAxBx
h
i
i
n
iixj
ji
i
m
() () ,where () () () ()
1
1
1
=
−
=
(2.17)
where
Ax wx
i
e
ij
ik
k
m
i
n
() ()
11
∑∑
[]
=
==
Bx wxP
i
e
ij
i
n
() ()
1
∑
[]
=
=
(2.18)
The necessary condition to get the nonsingular
matrix is the existence
of m nodes at least in the local interpolation domain of
. The approxi-
mate derivative of the function is computed by differentiating p(x) with
respect to x, by considering
as a constant, and given as
u
x
p
x
a
x
x
x