how to use mixed boundary condition?

Question

Hi there,

In a time-dependent problem, u and p are two independents. Is it possible to implement a boundary condition like:

u*p = Constant(1.0)

Actually, what kind of boundary is it? is it called mixed boundary condition?

Answer 1

To address your question of a "Mixed" boundary condition - typically, a domain consisting of both Dirichlet and Neumann boundary conditions are most often referred to as Boundary Value Problems with Mixed Boundary Conditions.

However, so called Robin boundary conditions - which incorporate some (linear) combination of the Dirichlet and Neumann conditions - are Mixed boundary conditions as well.

I refer to linear in parentheses above, since it seems you seem to be trying to combine them in a non-linear manner. Is there no alternative way in which you can formulate this boundary value problem ? Maybe use the boundary condition as a constraint instead ? Or a change of variables ?