Chapter 8.3, Problem 18CP

Solve the Laplace equation with Dirichlet boundary conditions from Exercise 13 on $[0,1]\times [0,1]$ with $T_0=0$ and $T_1=10$ using (a) a finite difference approximation and (b) the Finite Element Method. Make log-log plots of the error at particular locations in the rectangle as a function of step sizes $h=k=2^{-p}$ for p as large as possible Explain any simplifications you are making to evaluate the correct solution at those locations.