Elliptic2D

Solves the 2D Poisson equation with Robin boundary conditions on a nonuniform grid.

\[ \nabla^2 u(x,y) = f(x,y) \]

with \(x\in[0,10], y\in[0,10]\), and

\[\begin{split} f(x,y) = \begin{cases} (x-0.5)^2+(y-0.5)^2 & \text{ along boundaries } \\ 4 & \text{ otherwise } \end{cases} \end{split}\]

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).