This preview shows page 1. Sign up to view the full content.
HOMEWORK 3: ERROR ESTIMATION AND ADAPTIVE MESHING
•
Consider the boundary value problem
d
dx
±
A
1
du
dx
²
=
f
(
x
),
A
1
= 1, with
domain Ω = (0
,L
),
L
= 1, and solution
u
(
x
) = cos(19
πx
4
).
•
Compute the ﬁnite element solution
u
N
to this problem using linear
equalsized elements. Determine how many elements are needed in
order to achieve
e
N
def
=

u

u
N

A
1
(Ω)

u

A
1
(Ω)
≤
TOL
= 0
.
05
,

u

A
1
(Ω)
def
=
s
Z
Ω
du
dx
A
1
du
dx
dx
•
Plot
I
versus
E
I
, where
E
2
I
def
=
1
h
I

u

u
N

2
A
1
(Ω
I
)
1
L

u

2
A
1
(Ω)
.
Here
I
is the element index,
h
I
is the length of element
I
, and

u

2
A
1
(Ω
I
)
def
=
Z
Ω
I
du
dx
A
1
du
dx
dx.
•
Modify your code from HW 1 so that it can automatically reﬁne the
mesh the following criterion:
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 08/01/2008 for the course ME 180 taught by Professor Zohdi during the Spring '08 term at University of California, Berkeley.
 Spring '08
 ZOHDI

Click to edit the document details