JCP paper on linear elasticity (2021)¶

📄 Y. Zhang, Joël Fisser, Marc Gerritsma, A hybrid mimetic spectral element method for three-dimensional linear elasticity problems, Journal of Computational Physics 433 (2021) 110179.

You can download this paper (🌱 open access) at doi.org/10.1016/j.jcp.2021.110179.

This paper should be cited as shown at cite as.

Corrections¶

Because of my carelessness, there are some typos/errors in this paper and below I make corrections to those. Please excuse me for the inconveniences.

❌ typo-1¶

📍: on page 14, in Section 5.2 Manufactured solution

The mapping

\mathring{\Phi} : \mathring{\Omega} \to \Omega

is given as

\begin{Bmatrix}
    x\\y\\z
\end{Bmatrix} =
\mathring{\Phi}(r,s,t) =
\begin{Bmatrix}
\Phi^x(r,s,t)\\
\Phi^y(r,s,t)\\
\Phi^z(r,s,t)
\end{Bmatrix}=
\begin{Bmatrix}
r + c \sin(\pi r)\sin(\pi s)\sin(\pi t)\\
s + c \sin(\pi r)\sin(\pi s)\sin(\pi t)\\
t + c \sin(\pi r)\sin(\pi s)\sin(\pi t)
\end{Bmatrix},

which is not correct.

The correct mapping should be

\begin{Bmatrix}
    x\\y\\z
\end{Bmatrix} = \mathring{\Phi}(r,s,t) =
\begin{Bmatrix}
\Phi^x(r,s,t)\\
\Phi^y(r,s,t)\\
\Phi^z(r,s,t)
\end{Bmatrix}=
\begin{Bmatrix}
r + \frac{1}{2}c \sin(2\pi r)\sin(2\pi s)\sin(2\pi t)\\
s + \frac{1}{2}c \sin(2\pi r)\sin(2\pi s)\sin(2\pi t)\\
t + \frac{1}{2}c \sin(2\pi r)\sin(2\pi s)\sin(2\pi t)
\end{Bmatrix}.

For a complete Python implementation of this mesh, see crazy_mesh.py.

❌ typo-2¶

📍: on page 17, in Section 5.2.1 Cracked arch bridge

This subsection better be a Section; 5.3 Cracked arch bridge.


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