For many problems with a known exact solution, the right hand side of the differential equation is given as f (or f₁ or some other related form) and the right hand side of the boundary condition is given as g (or a related form). In this case the right hand side is determined by applying the operator to the exact solution.

Poisson's Equation (in 2D) is -u_xx - u_yy = f, with the obvious modifications for other numbers of dimensions.

Laplace's Equation is Poisson's Equations with f = 0.

The Dirichlet boundary condition is u = g.

The Neumann boundary condition is ∂u/∂n = g where n is the outward unit normal.

The natural boundary condition for (for example) -∇·(p∇u)=f is p∇u·n=g where n is the outward unit normal vector.
When p=1, the natural boundary conditions are Neumann.

The unit interval is (0,1).
The unit square is (0,1)X(0,1).
The unit cube is (0,1)X(0,1)X(0,1).