Elliptic3D#
Similar to minimal_poisson2D, this solves a 3D problem using mimetic Laplacian, where one side of the domain is set to 100, and allowed to diffuse.
\[
\nabla^2 u(x,y,z) = f(x,y,z)
\]
with \(x\in[0,5], y\in[0,6], z\in[0,7]\), and
\[\begin{split}
f(x,y,z) = \begin{cases}
100 & \text{ if z = 0} \\
0 & \text{ otherwise }
\end{cases}
\end{split}\]
The boundary conditions are given by
\[
au + b\nabla u = g
\]
with \(a=1\), \(b=0\), and \(g=0\).
This corresponds to the call to robinBC3D of robinBC3D(k, m, 1, n, 1, o, 1, 1, 0).