Elliptic2D Case 2#
Solves the 2D Poisson equation with Robin boundary conditions on a nonuniform sinusoidal grid.
\[
\nabla^2 u(x,y) = f(x,y)
\]
with \(x\in[-\pi, 2\pi], y\in[-\pi, \pi]\), and
\[\begin{split}
f(x,y) = \begin{cases}
\sin(x)\sin(y) & \text{ along boundaries } \\
-2\sin(x)\sin(y) & \text{ otherwise }
\end{cases}
\end{split}\]
The boundary conditions are given by
\[
au + b\nabla u = g
\]
with \(a=1\), \(b=0\), and \(g=0\), which is equivalent to Dirichlet conditions along each boundary.
This corresponds to the call to robinBC2D of robinBC2D(k, m, 1, n, 1, 1, 0).