Dear FreeFem users and developers,

I need to solve the eigenequation of the Laplace operator in two

spatial dimensions, with a homogeneous Robin boundary condition:

Laplace phi = lambda phi in the domain

a phi + b \partial_n phi = 0 at the boundary

int phi^2 = 1 integral over the domain

I have seen in the documentation and the examples that FreeFem allows

to solve the eigenequation with Dirichlet boundary conditions, and I

also found some hints on Neumann bc. In some sense, I need everything

between these two: The parameters a and b take any values (constant

for the moment, space-dependent later).

Is there a way to formulate this problem in FreeFem? I searched the

documentation and thought about it, but I see no way. Maybe you have

an idea?

If I understand the documentation correctly, Dirichlet bc are

implemented by penalisation, that is some corresponding entries in the

matrices of the discretised eigensystem are set to so large values

that the values of phi can only be zero in the end. Can this strategy

be extended to arbitrary linear boundary conditions? Is the FreeFem

problem language ready to formulate such a penalisation (beyond

Dirichlet)?

All hints and good ideas are welcome,

Michael