Elliptic2D Nodal Curv

Solves the 2D Poisson equation with Robin boundary conditions on a curvilinear grid using the nodal mimetic operator. This requires manually setting the boundary condition in the Laplacian, as there is no boundary condition operator for the nodal curvilinear operators.

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

with \(x\in[0,50], y\in[0,50]\), 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

\[ au + b\nabla u = g \]

The Octave code uses the function boundaryIdx2D to find the correct locations for boundary condition weights in the nodal Laplacian. The code then sets the appropriate values to \(0\) or \(1\).