This is a Poisson 2D equation Python solver using FEM.

The main file is <PoissonSolver2D.py>

The Poisson eguation (with a Robin general boundry condition) given as following:

-\nabla.(a(xy)\nabla{u}) = f(x,y)         in \Omega
-n.(a(xy)\nabla{u}) = k(u - g_D) - g_N    in \partial{\Omega}

Where a(x,y) > 0, f(x,y), g_D and g_N are given functions.

With

The domain is [-1,1]^2
f(x,y) = 0 
a(x,y) = 1
k = 1
g_D sin(x+y)^2
g_N =1 on x = -1  and 0 elsewhere

we have the approximated solution u_h:

The stiffness matrix:

which evaluated on the following mesh:

Maged Shaban
magshaban[at]gmail.com