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Neumann boundary condition in 2D
Use ideas from 1D! Example: \frac{\partial u}{\partial n} at y=0 ,
\frac{\partial u}{\partial n} = -\frac{\partial u}{\partial y}
Boundary condition discretization:
[-D_{2y} u = 0]^n_{i,0}\quad\Rightarrow\quad \frac{u^n_{i,1}-u^n_{i,-1}}{2\Delta y} = 0,\ i\in\Ix
Insert u^n_{i,-1}=u^n_{i,1} in the stencil for u^{n+1}_{i,j=0} to
obtain a modified stencil on the boundary.
Pattern: use interior stencil also on the bundary, but replace
j-1 by j+1
Alternative: use ghost cells and ghost values
