Elliptic2D Nodal Curv Sinusoidal

Solves the 2D Poisson equation with Robin boundary conditions on a curvilinear sinusoidal 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 \(x\in[-\pi, 2\pi], y\in[-\pi, \pi]\), and

\[\begin{split} f(x,y) = \begin{cases} \sin(x)+\cos(y) & \text{ along boundaries } \\ -\sin(x) - \cos(y) & \text{ otherwise } \end{cases} \end{split}\]

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. The MATLAB/ OCTAVE code uses the function boundaryIdx2D to find the correct locations for the weights of the boundary condition in the Laplacian node. The code then sets the appropriate values to \(0\) or \(1\).