<s>
Weakened	B-Algorithm
weak	I-Algorithm
form	I-Algorithm
(	O
or	O
W2	O
form	O
)	O
is	O
used	O
in	O
the	O
formulation	O
of	O
general	O
numerical	O
methods	O
based	O
on	O
meshfree	B-Algorithm
methods	I-Algorithm
and/or	O
finite	B-Application
element	I-Application
method	I-Application
settings	O
.	O
</s>
<s>
Our	O
discussion	O
is	O
also	O
most	O
convenient	O
in	O
reference	O
to	O
the	O
well-known	O
weak	B-Algorithm
and	I-Algorithm
strong	I-Algorithm
form	I-Algorithm
.	O
</s>
<s>
In	O
a	O
weak	B-Algorithm
formulation	I-Algorithm
,	O
we	O
create	O
linear	O
and	O
bilinear	O
forms	O
and	O
then	O
search	O
for	O
a	O
particular	O
function	O
(	O
an	O
approximate	O
solution	O
)	O
that	O
satisfy	O
the	O
weak	O
statement	O
.	O
</s>
<s>
In	O
a	O
discrete	O
form	O
(	O
such	O
as	O
the	O
Finite	B-Application
element	I-Application
method	I-Application
,	O
or	O
FEM	O
)	O
,	O
a	O
sufficient	O
requirement	O
for	O
an	O
assumed	O
displacement	O
function	O
is	O
piecewise	O
continuous	O
over	O
the	O
entire	O
problems	O
domain	O
.	O
</s>
<s>
The	O
development	O
of	O
systematic	O
theory	O
of	O
the	O
weakened	B-Algorithm
weak	I-Algorithm
form	I-Algorithm
started	O
from	O
the	O
works	O
on	O
meshfree	B-Algorithm
methods	I-Algorithm
.	O
</s>
