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Meshless Methods and Their Numerical Properties
book

Meshless Methods and Their Numerical Properties

by Hua Li, Shantanu S. Mulay
February 2013
Intermediate to advanced content levelIntermediate to advanced
447 pages
14h 16m
English
CRC Press
Content preview from Meshless Methods and Their Numerical Properties
Recent developments of meshless methods 83
3.3.3 Examples for validation
In this subsection, several 1-D and 2-D examples of ordinary and partial
differential equations that are always associated with mechanics problems
are solved to demonstrate the performance of the PWLS method. The fol-
lowing norms are dened as the error indicators,
=
∑−
=
=
e
N
uu
u
1| |
||
i
N
ii
i
N
i
0
1
exact num
1
exact
(3.90)
where u
i
exact
and u
i
num
are the exact and numerical approximate solutions
of the function, respectively. The errors for the rst-order derivatives of the
function are dened as e
1x
and e
1y
, respectively
=
∑−
=
∑−
=
=
=
=
e
N
uu
u
e
N
uu
u
1| |
||
,
1
||
||
x
i
N
ix ix
i
N
ix
y
i
N
iy iy ...
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Publisher Resources

ISBN: 9781466517462