We introduce goal-oriented estimates of numerical approximation errors of the automatic variationally stable finite element (AVS-FE) method [1] for the numerical analysis of convection-dominated second order boundary value problems. The AVS-FE method is a hybrid continuous-discontinuous Petrov-Galerkin (DPG) method [2] and uses standard FE trial functions that are piecewise globally continuous polynomials. The test functions, however, are piecewise discontinuous and computed by using the DPG approach resulting in unconditionally stable FE discretizations. Remarkably, the support of each discontinuous test function is identical to its corresponding continuous trial function and the element restrictions of the test functions contribution can be computed completely locally (i.e. decoupled). Additionally, numerical evidence indicates that the computation of the (optimal) test functions is achieved with sufficient accuracy by using the same polynomial order of approximation as used for the trial functions. As in every other DPG formulation, the resulting algebraic system is symmetric and positive definite, allowing to use simple iterative strategies to compute the numerical solution. Goal oriented estimates of the numerical approximation error can subsequently be obtained by applying a residual-based error estimation technique [3] to the AVS-FE method. Numerical examples are shown for convection-dominated diffusion problems. REFERENCES [1] V. M. Calo, A. Romkes, and E. Valseth, “Automatic Variationally Stable Analysis for FE Computations: An Introduction”. In: G. R. Barrenechea, J. Mackenzie (Eds.), Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018, Springer International Publishing, pp. 19–43, (2020). [2] L. Demkowicz and J. Gopalakrishnan, “Analysis of the DPG Method for the Poisson Equation”, SIAM Journal on Numerical Analysis, Vol. 49 (5), pp. 1788–1809, (2011). [3] J. T. Oden and S. Prudhomme, “Estimation of Modeling Error in Computational Mechanics”, Journal of Computational Physics Vol. 182 (2), pp. 496 – 515, (2002).