Develop the finite element equation set for a differential equation (given below, with appropriate boundary conditions) and use your derived element to approximate the solution to the differential equation on the region bounded by the given boundary conditions.

Use a bilinear interpolation function (that is, the approximation will be of the form a + bx + cy + dxy, where a, b, c, d are constants to be found for each element, and x, y are independent spatial variables).

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A minimum of 9 nodes will be required; more may be necessary, if comparison of exact to approximate solutions is poor. You will be well advised to use a computer program such as Matlab for setting up and solving the global set. You may use Matlab more extensively if you wish, but all work done in Matlab must be properly explained (for clarity, to assist in grading.)

The specific differential equation to be approximately solved is:

For comparison of FE results to exact results: the exact solution to this PDE with these boundary conditions is

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