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{\bf EGN 5456 \hfill Intro to Computational Mechanics \hfill 4/3/90 }\\
{\it Open notes \hfill Leon Van Dommelen \hfill 2:30-3:45 pm }
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\begin{enumerate}

\item
Describe a Galerkin solution to
$$-u_{xx} + 2 u =1$$
$$u(-1) = u(1) = 0$$
Find the truncation error in the results.

\item
Discuss the variational formulation of the {\it fourth} order
problem
$$u_{xxxx} + u = 1$$
$$u(0) = u_x(0) = u(1) = u_x(1) = 0$$
Note that all these boundary conditions are essential for a fourth
order
equation. So what boundary conditions would you impose on $v(x)$?
What would be the bilinear and linear operators?  What smoothness
would
you impose on the solution.  Would linear splines work?

\end{enumerate}

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