Using three linear elements a linear element has two nodes

Question

Finite Element Weighted Residual Solution of Differential Equations

Consider the differential equation 

d²p/dx²  + p + x = 0     0 < x < 1

Subjecto boundary conditions

p(0) = 0; p(1) = 0

The exact solution to this problem is written as

p(x) = (sinx/sin1) -  x

Determine the following finite element solutions to this problem

(a) Using three linear elements. A linear element has two nodes with a linear interpolation of the field variable between these nodes

(b) Using one three-node element for the entire domain

(c) Using two three-node elements for the entire domain

The solution using two linear elements was provided in class, Plot all the solutions (including the exact sotuiion) on a single graph to compare solutions.