Adjoint error estimation and grid adaptation for functional outputs: application to quasi-one-dimensional flow

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Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics (2011, methodology): “(24), this formof error estimate has also been used with both finite element [7,40,70–72] and finite volume [39,65,66,73–79] discretizations.”
Grid adaptation for functional outputs: application to two-dimensional inviscid flows (2002, methodology): “An appropriate definition for I H h depends on the underlying discretization method [ 17 ].”
Verification and Validation in Computational Fluid Dynamics (2002, background): “Venditti and Darmofal [332] discuss the coupling of error estimation and adaptive gridding to reduce numerical errors in such computed functionals.”
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (2014, methodology): “In contrast, most implementations of the dualweighted residual method require an approximation to the adjoint on a refined space [95, 96, 97, 98, 99].”
An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids (2004, background): “The test cases examined in [27,28], and [30–32] clearly demonstrate the potential of using such an approach to grid adaptation.”