Math 6420 • PDE

Consider the problem \(u''(x)=f(x)\), on \((0,1)\), with boundary conditions
\(u'(0)=u'(1)=0\).
\begin{enumerate}
\item[(a)] Write down the weak formulation of the problem.

\item[(b)] Using a piecewise linear finite element basis with uniform grid size \(h\), use the
Galerkin method to find a finite-dimensional (matrix) approximate representation for the
problem. Do not solve the equations.

\item[(c)] Neither of the problems (a) and (b) have unique solutions in general. Explain why
not, and describe what can be done to correct the deficiency.
\end{enumerate}