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 MATLAB/ 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 \(1\).