Question 5 only!!!

N 3. Let [0, L] and a positive integer N be given. Construct x1 = 0, XN+1 = L, and Xi+1 = Xi + hi, for given subinterval lengths {hi}\, such that hi = L. Then set Ti = (Xi, Xi+1), and Dn = {ti}N1. Define the following functions di : [0, L] [0, 1], for every i = 1, 2, ... ,N +1: i=1 Po (***). * E T1, 01(x) = = 0, elsewhere, X 11-1 P1 x E Ti-1, hi-1 di(x) = Po 2 - Xi hi The ), , = 2, ...,N, 0, elsewhere, P1 2 (), f X IN hn 0 TN, ON+1(2) = elsewhere. The space of piecewise linear functions and continuous over Dh can be defined as Vh span{Pi}^11 As stated in class, h max {hi}. 1