Q4: Consider the problem -((1+x)u') = 0, x =I= [0,1], u(0) = 0, u'(1) = 1 Divide the interval I into three subintervals of equal length h =1/3 and let V be the corresponding space of continuous piecewise linear functions vanishing at x = 0,1. Find the variational form and finite element method Verify that the stiffness matrix A is given by: 1 16 -9, 0. 3 -11 11 A = 2 - -9 20 0 -11 Q5: Consider the semi discrete finite element solution is dt (u(t), v) ,v) + a(u(t),v) = (f(t), v) vv EV Let a(u(t), v) be v-elliptic and continues bilinear form, prove that the stability estimate satisfies ||u(T)||ea||u(0)|| +fear-t) ||f|| dt Q6: Given the triangulation of figure, determine the basis function and compute the integrals: So z dx, Jo 41 42 dx, o fdx. 4243dx, V1.2 dx. 3 (0,1) 2 (0,0) (1,0)