NUMERICAL PARTIAL DIFFERENTIAL EQUATIONS, Mathematics

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Our objective is solve the following fourth-order BVP:
(a(x)u'' )'' = f (x)
u(0) = u(1)=0
u(0)' = u(1)'=0

(a) Give the variational formulation of the above BVP.
(b) Describe the appropriate discrete space.
(c) Sketch the graph of a typical basis function.
(d) Derive the discrete formulas.
(e) Write a FEM matlab code for the above BVP and construct an example to test it. Sketch the graph of the exact solution vs the computed solution.

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