Controlling approximation error

Publisher Summary The approximation error is bounded by the interpolation error in the case of a two-dimensional test case of laminar flow over a NACA0012 airfoil. This chapter illustrates how a numerical solution over a fine and adapted mesh serves as the exact solution. The interpolation error has been successfully approximated by a reconstruction of the Hessian of the numerical solution. The convergence of the approximation error and the convergence of the gradient are plotted by using the fine mesh as the exact solution. Finally, anisotropic adapted meshes are generated that conformed to the tensor metric space stemming from the reconstruction of the Hessian of the numerical solution. These adapted meshes are shown to equidistributed the interpolation error by comparing them to a solution computed on a very fine and adapted mesh. The reconstructed Hessian is a valid error estimator.