1.Develop a two-dimensional finite element program using the fully implicit time approximation scheme and bilinear rectangular elements, and using input data . The computer program should incorporate the following features:

(a) construct the element capacitance and matrix cðeÞ , the element characteristic matrix kðeÞ , and element force vector f ðeÞ based on the bilinear rectangular element;

(b) assemble the global system of equations and

(c) solve the global system using the Gauss elimination solver with refined grid size distributions as 4 4, 6 6, and 8 8 using this code. Present the temperature distribution along with the percent relative error for the vertical center line with refined grid size distributions at different time steps.