Coarse grid correction
Content 
In general we would apply coarse grid corrections until a norm of the residual is below a given threshold (which depends on an error estimator). In this exercise we apply just a fixed number of iterations to see how the residual decreases.
Exercise
Apply three iterations of the coarse grid correction:

Plot the residual of the initial guess and

the residual after each iteration.

Plot the final approximate solution
Use a test case with exact solution \(u(x) = \sin{2 \pi e^{2x}}\).