I would like to write a simple finite element solver in python in order to solve 2D Poisson equation and then visualize it.

$$ -\nabla^{2} u(x,y)=f(x,y), \quad x,y \quad in \quad \Omega\\ u(x,y) = u_D (x,y), \quad x,y \quad in \quad \partial \Omega $$

Why do I wanna do that? I would like to learn how write a simple finite element solver using python and since the Poisson equation is like the "hello world!" for the computational science I would like to work with it. I already had look at FEniCS, deal.II and some other solvers but as I mentioned I would like to write my own simple script.

Would you introduce any simple to understand source where I can learn how to solve and code this equation using finite element method?



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