Dirichlet and Boundary conditions in Darcy tutorial.

[amartinhuertas]

Hi @fverdugo ... I think that the Dirichlet and Neumann Boundary conditions are flipped in the Darcy's tutorial + RT FEs.

In particular, in the Darcy problem, one imposes the trace of the pressure in the Dirichlet boundary, and the normal component of the flux in the Neumann boundary. Indeed, Dirichlet boundary conditions are natural boundary conditions (i.e., imposed weakly) for Darcy, and Neumann boundary condition are essential boundary conditions for Darcy (i.e., imposed strongly).

See, e.g., pag. 153 of

https://team-pancho.github.io/documents/anIntro2FEM_2015.pdf

Is there anything I am missing here? Do you agree? I can help with the changes required to fix this, if needed.

[fverdugo]

I always have had this question... perhaps @santiagobadia can tell better.

If you see the darcy problem as a mixed poisson equation, then the notation in the pdf makes sense, but it is strange to call "Neumann" something that you impose strongly... Perhaps for this reason, we have flipped the notion of Dirichlet and Neumann.

In any case, I fill more confortable with the notation you prupose @amartinhuertas since i like to see darcy as a mixed poisson equation.