Consider the scalar  PDE for $u$ with Dirichlet boundary conditions:$\mathrm{div}(\mathcal{K}\nabla u) = f\; \forall x\;  \in \Omega \subset R^2$, $u = 0 \; \forall \; x\;\in \partial\Omega$where $\mathcal{K} \in R^{2\times 2}$ is positive definite symmetric.For a start I assume $\Omega$ is the unit square with a uniform rectangular mesh.EDIT: I edited the question following Jed's comment to make it more specific.If $\mathcal{K}$ is diagonal, it is simple enough. When it is not, I see that there it will require  a computation of the secondary gradient (gradient along the face). How is that usually done ? And what I should do when I am near the boundary in this case ?
finite volume for diffusion equation with anisotropic (tensor) coefficient
finite difference;finite volume;poisson;advection diffusion;tensor