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Commit 88f9e8ca authored by Steffen Müthing's avatar 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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1 merge request!40Bugfix/fix typo
......@@ -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@Unpublished{BastianII,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_ss2014/num2.pdf}} },
note = {{\small\url{https://conan.iwr.uni-heidelberg.de/data/teaching/finiteelements_ws2017/num2.pdf}} },
year = {2014},
}
......@@ -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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