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Chris Bickford Introduction to Finite Elements HW #5; Problem 3 MAPLE: Maple software was used to solve for the exact solution. The value at u(0.2, 0) is 1 and the value at u(0.2, 0.15) is 0 for the exact solution. The value at u(0.3, 0.15) is 0.95 for the exact solution. See attached maple sheet for more details. ABAQUS FEA CODE: ABAQUS 6.14 software was used to perform finite element analysis (FEA) to obtain an approximate solution for problem (2). A 2-dimensional transient heat transfer analysis was performed assuming no boundary conditions on the top (x , 0.5) and bottom (x, 0.5) edges, which effectively makes the problem one-dimensional. The temperature over the domain is close to zero after 1 second, which is approaching the exact solution. Figure 2 shows a time history of the value at x = 0.2, which starts at one and begins to approach zero at about t = 0.40s, which is later than the exact solution (t=0.15s). Figure 1 FEM Mesh Density Figure 2 Time-History of the Value at x = 0.2: Quadratic Element Type Figure 3 Time-History of the Value at x = 0.2: Exact Solution