  The spectral deferred correction method is a variant of the deferred
correction method for solving ordinary differential equations. A benefit of
this method is that is uses low order schemes iteratively to produce a high
order approximation. In this paper we consider adjoint-based a posteriori
analysis to estimate the error in a quantity of interest of the solution. This
error formula is derived by first developing a nodally equivalent finite
element method to the spectral deferred correction method. The error formula is
then split into various terms, each of which characterizes a different
component of the error. These components may be used to determine the optimal
strategy for changing the method parameters to best improve the error.
