  This paper is concerned with goal-oriented a posteriori error estimation for
nonlinear functionals in the context of nonlinear variational problems solved
with continuous Galerkin finite element discretizations. A two-level, or
discrete, adjoint-based approach for error estimation is considered. The
traditional method to derive an error estimate in this context requires
linearizing both the nonlinear variational form and the nonlinear functional of
interest which introduces linearization errors into the error estimate. In this
paper, we investigate these linearization errors. In particular, we develop a
novel discrete goal-oriented error estimate that accounts for traditionally
neglected nonlinear terms at the expense of greater computational cost. We
demonstrate how this error estimate can be used to drive mesh adaptivity. We
show that accounting for linearization errors in the error estimate can improve
its effectivity for several nonlinear model problems and quantities of
interest. We also demonstrate that an adaptive strategy based on the newly
proposed estimate can lead to more accurate approximations of the nonlinear
functional with fewer degrees of freedom when compared to uniform refinement
and traditional adjoint-based approaches.
