Consider a finite element with three nodes, as shown in the figure. When the solution is approximated using \(u(x)=N_{1}(x) u_{1}+N_{2}(x) u_{2}+N_{3}(x) u_{3}\), calculate the interpolation functions \(N_{1}(x), N_{2}(x)\), and \(N_{3}(x)\). Hint: Start with an assumed solution in the following form: \(u(x)=c_{0}+c_{1} x+c_{2} x^{2}\).

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1 X 1 m u2 2 1 m 3