  Solutions to the governing partial differential equations obtained from a
discrete numerical scheme can have significant errors, especially near shocks
when the discrete representation of the solution cannot fully capture the
discontinuity in the solution. A recent approach to shock tracking [1, 2] has
been to implicitly align the faces of mesh elements with the shock, yielding
accurate solutions on coarse meshes. In engineering applications, the solution
field is often used to evaluate a scalar functional of interest, such as lift
or drag over an airfoil. While functionals are sensitive to errors in the flow
solution, certain regions in the domain are more important for accurate
evaluation of the functional than the rest. Using this fact, we formulate a
goal-oriented implicit shock tracking approach that captures a segment of the
shock that is important for evaluating the functional. Shock tracking is
achieved using Lagrange-Newton-Krylov-Schur (LNKS) full space optimizer, with
the objective of minimizing the adjoint-weighted residual error indicator. We
also present a method to evaluate the sensitivity and the Hessian of the
functional error. Using available block preconditioners for LNKS [3, 4] makes
the full space approach scalable. The method is applied to test cases of
two-dimensional advection and inviscid compressible flows to demonstrate
functional-dependent shock tracking. Tracking the entire shock without using
artificial dissipation results in the error converging at the orders of
$\mathcal{O}(h^{p+1})$.
