No Normal Flow Boundary Condition

[hgpeterson]

Hello,

I'm wondering how one can implement a no-normal-flow boundary condition (u ⋅ n = 0) on a general mesh? It looks like the boundary condition was written out in the Darcy equation tutorial, but in the end, the lines

uD = VectorValue(0.0,0.0)
U = TrialFESpace(V,uD)

just set u = 0 on the boundary. For this square geometry, it would be simple to set u ⋅ n = u₂ = 0, but what about for a general mesh with the normal vector n a function of space?

Thanks.

[amartinhuertas]

You can define uD as a Julia function that given the coordinates of a point in the boundary, returns a VectorValue instance with the result of evaluating the point.

Note that for Hdiv-conforming spaces, e.g., Raviart-Thomas spaces, the implementation of such conditions is relatively easy as these can be imposed strongly.

When you have other types of spaces (not sure if this is the case), such as, e.g., H1-conforming spaces discretized with Lagrangian FEs, the imposition of such conditions is more involved. In such a case, you may use, e.g., weak Nitsche boundary conditions, or Lagrange multipliers.