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PDELab
dune-pdelab-tutorials
Commits
88f9e8ca
Commit
88f9e8ca
authored
7 years ago
by
Steffen Müthing
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Merge branch 'bugfix/fix-typo' into 'master'
Bugfix/fix typo See merge request
!40
parents
97d1aee0
19ec9a14
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!40
Bugfix/fix typo
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tutorial00/doc/tutorial00.bib
+2
-2
2 additions, 2 deletions
tutorial00/doc/tutorial00.bib
tutorial00/doc/tutorial00.tex
+3
-3
3 additions, 3 deletions
tutorial00/doc/tutorial00.tex
with
5 additions
and
5 deletions
tutorial00/doc/tutorial00.bib
+
2
−
2
View file @
88f9e8ca
...
...
@@ -17,7 +17,7 @@ year = {2009},
author
=
{K. Eriksson and D. Estep and P. Hansbo and C. Johnson}
,
title
=
{Computational Differential Equations}
,
publisher
=
{Cambridge University Press}
,
note
=
{{\small\url{http://www.csc.kth.se/~jjan/
private
/cde.pdf}} }
,
note
=
{{\small\url{http://www.csc.kth.se/~jjan/
transfer
/cde.pdf}} }
,
year
=
{1996}
,
}
...
...
@@ -85,7 +85,7 @@ year = {2009},
@Unpublished
{
BastianII
,
author
=
{P. Bastian}
,
title
=
{Lecture Notes on Scientific Computing with Partial Differential Equations}
,
note
=
{{\small\url{http://conan.iwr.uni-heidelberg.de/teaching/
numerik2_s
s201
4
/num2.pdf}} }
,
note
=
{{\small\url{http
s
://conan.iwr.uni-heidelberg.de/
data/
teaching/
finiteelements_w
s201
7
/num2.pdf}} }
,
year
=
{2014}
,
}
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tutorial00/doc/tutorial00.tex
+
3
−
3
View file @
88f9e8ca
...
...
@@ -494,11 +494,11 @@ tools:
\begin{enumerate}
[Tool 1)]
\item
Transformation formula for integrals. For
$
T
\in\mathcal
{
T
}_
h
$
we have
\begin{equation*}
\int
_
T y(x)
\,
dx =
\int
_{
\hat
T
}
y(
\mu
_
T(
\hat
x)) |
\det
B
_
T|
\,
dx .
\int
_
T y(x)
\,
dx =
\int
_{
\hat
T
}
y(
\mu
_
T(
\hat
x)) |
\det
B
_
T|
\,
d
\hat
x .
\end{equation*}
\item
Quadrature formula. The midpoint rule reads
\begin{equation*}
\int
_{
\hat
T
}
q(
\hat
x)
\,
dx = q(
\hat
S
_
d) w
_
d
\int
_{
\hat
T
}
q(
\hat
x)
\,
d
\hat
x = q(
\hat
S
_
d) w
_
d
\end{equation*}
where
$
\hat
S
_
d
$
is the center of mass of the reference simplex
$
\hat
T
^
d
$
and
$
w
_
d
$
is the volume of
$
\hat
T
^
d
$
. This quadrature formula is exact for linear
...
...
@@ -538,7 +538,7 @@ interior vertices than boundary vertices we may first compute $(b)_i = l(\phi_i)
for
{
\em
all
}
$
i
\in\mathcal
{
I
}_
h
$
and then overwrite the entries on the boundary
with
$
(
b
)
_
i
=
g
(
x
_
i
)
$
. Moreover, when considering the global index
$
i
$
only the pairs in the set
$$
C
(
i
)
=
\{
(
T,m
)
\in\mathcal
{
T
}_
h
\times\{
0
,
\ldots
,d
\}
\,
:
\,
g
(
T,
m
)=
i
\}
$$
$$
C
(
i
)
=
\{
(
T,m
)
\in\mathcal
{
T
}_
h
\times\{
0
,
\ldots
,d
\}
\,
:
\,
g
_
T
(
m
)=
i
\}
$$
contribute to the computation, which can be carried out in the following way:
\begin{align*}
(b)
_
i
&
= l(
\phi
_
i) =
\int
_
\Omega
f
\phi
_
i
\,
dx
&&
\text
{
(definition)
}
\\
...
...
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