FreeFem++

// Poisson equation solver using FreeFem++
// -Delta(u) = f in Omega, u = 0 on boundary

// Define a square mesh with 20x20 grid
mesh Th = square(20, 20);

// P1 finite element space (piecewise linear)
fespace Vh(Th, P1);
Vh u, v;

// Right-hand side function
func f = 1.0;

// Variational formulation (weak form)
problem Poisson(u, v) =
    int2d(Th)(dx(u)*dx(v) + dy(u)*dy(v))
    - int2d(Th)(f*v)
    + on(1, 2, 3, 4, u=0);  // homogeneous Dirichlet BC

// Solve the problem
Poisson;

// Output solution statistics
cout << "Solution computed successfully." << endl;
cout << "u max = " << u[].max << endl;
cout << "u min = " << u[].min << endl;