I'm searching for examples of Helmholtz or Poisson equations with Neumann and Dririchlet boundary conditions and their exact solutions. Is there any database of them on the web?

Thank you!

Hi,
I have tried to search the same but unable to locate it ,sorry.

Hi,

You can try this.
(d^2/dx^2 + d^2/dy^2)u = f
where f = -2*x*(2-x) - 2*y*(2-y)
& 0 < x,y < 2

Boundary conditions:
u = 0 for x=0, x=2, y=0, y=2

Exact solution is:

u = x*(2-x)*y*(2-y)