Subdomains and boundary conditions
Hans Petter Langtangen, Anders Logg · 2016
Let’s return to the Poisson problem from Chap. 2 and see how to extend the mathematics and the implementation to handle a Dirichlet condition in combination with a Neumann condition. The domain is still the unit square, but now we set the Dirichlet condition $$u=u_{\mathrm{D}}$$ at the left and right sides, $$x=0$$ and $$x=1$$ , while the Neumann condition $$\begin{aligned} -{\partial u\over \partial n}=g \end{aligned}$$ is applied to the remaining sides $$y=0$$ and $$y=1$$ .