Adjoint and defect error bounding and correction for functional estimates, AIAA Paper 2003; 3846

We present two error estimation approaches for bounding or correcting the error in func-tional estimates such as lift or drag. Adjoint methods quantify the error in a particular output functional that results from residual errors in approximating the solution to the partial differential equation. Defect methods can be used to bound or reduce the error in the entire solution, with corresponding improvements to functional estimates. The ap-proaches may be used separately or in combination to obtain highly accurate solutions with asymptotically sharp error bounds. The adjoint theory is extended to handle flows with shocks; numerical experiments confirm 4th order error estimates for a pressure integral of shocked quasi-1D Euler flow. Numerical results also demonstrate 4th order accuracy for the drag on a cusped lifting airfoil at subsonic conditions