On adjoint equations for error analysis and optimal grid adaptation in CFD - Giles, M (Unspecified, 1997)
This paper explains how the solutions of appropriate adjoint equations can be used to estimate the errors in important integral quantities, such as lift and drag, obtained from CFD computations. These error estimates can be used to obtain improved estimates of the integral quantities, or as the basis for optimal grid adaptation. The theory is presented for both finite volume and finite element approximations. For a node-based finite volume discretisation of the Euler equations on unstructured grids, the adjoint analysis makes it possible to prove second order accuracy. A superconvergence property is proved for a finite element discretisation of the Laplace equation, and references are provided for the extension of the analysis to the convection/diffusion and incompressible Navier-Stokes equations. This paper was presented at the symposium Computing the Future II: Advances and Prospects in Computational Aerodynamics to honour the contributions of Prof. Earll Murman to CFD and the aerospace community.