  Adjoint methods have gained popularity in recent years for driving adaptation
procedures which aim to reduce error in solution functionals. While adjoint
methods have been proven effective for functional-based adaptation, the
practical implementation of an adjoint method can be quite burdensome since
code developers constantly need to ensure and maintain a dual consistent
discretization as updates are made. Also, since most engineering problems
consider multiple functionals, an adjoint solution must be obtained for each
functional of interest which can increase the overall computational cost
significantly. In this paper, an alternative to adjoints is presented which
uses a sparse approximate inverse of the Jacobian of the residual to obtain
approximate adjoint sensitivities for functional-based adaptation indicators.
Since the approximate inverse need only be computed once, it can be recycled
for any number of functionals making the new approach more efficient than a
conventional adjoint method. This new method for functional-based adaptation
will be tested using the quasi-1D nozzle problem, and results are presented for
functionals of integrated pressure and entropy.
