High-order methods and mesh adaptation for Euler equations

In this paper, we point out a novel contribution of mesh adaptation to high-order methods for stationary and time-dependent problems. From theoretical results, we exhibit that mesh adaptation, based on an adjoint-free method, achieves a global second-order mesh convergence for numerical solutions with discontinuities in L(p) norm. To attain this result, it is mandatory to combine together all mesh adaptive methods developed in the previous work. This theoretical result is validated on 2D and 3D examples for stationary and time-dependent simulations. Copyright (C) 2008 John Wiley & Sons, Ltd.