# Thread: Analytical solution of the poisson equation

1. ## Analytical solution of the poisson equation

Hi,

Does anyone know how to solve the following for an analytical solution?

- nabla . sigma (u) = f

if

u = sin(pi*x)sin(pi*y)
v = sin(pi*x)sin(pi*y)

?
I know that I need to assign a value for u and v and then get values of x and y, but I'm not sure what to do afterwards!

Many thanks !

2. ## Re: Analytical solution of the poisson equation

Originally Posted by mojojojo17
Hi,
Does anyone know how to solve the following for an analytical solution?
- nabla . sigma (u) = f
if u = sin(pi*x)sin(pi*y)[ v = sin(pi*x)sin(pi*y)?
I know that I need to assign a value for u and v and then get values of x and y, but I'm not sure what to do afterwards!

3. ## Re: Analytical solution of the poisson equation

Sorry!

I was mainly looking for information on how to solve an elliptic PDE of the form
- nabla . sigma (u) = f
with the assigned values of u. (ignore the v for now)
so I would give a value to u, then find my x and y from u = sin(pi*x)sin(pi*y)
then, I would be able to find a value of f from that.
It is this step that I am confused about.
Sorry for any confusion in the above post!