We wish to solve a 2D ADR equation on a unit square, where the lower boundary (i.e. at y = 0) is itself a simple 1D PDE. For example,
$$ \frac{\partial u}{\partial t} = \nabla \cdot (\vec{a} u - D \nabla u) - ku $$
is defined on the whole domain, where $D$ and $k$ are constants, and the boundary conditions are mixed. Additionally, we have a separate PDE that must be solved, which is only defined on the lower boundary:
$$ \frac{\partial v}{\partial t} = u(\beta - v) - \alpha v $$
where $\alpha$ and $\beta$ are constants.
What we are wondering is: can FEniCS solve this 1D problem with the same mesh from the above 2D problem?
Any help is appreciated!