Mapping LSE method on a grid. Software architecture and performance gains

The chapter explores how least square extrapolation (LSE) can perform on a commercial code, without having any knowledge on the source code. It emphasizes this approach by using a basic network of workstation to compute the weighted solutions and then solves the minimization problem over the produce results. In computational fluid dynamics (CFD), a Posteriori error estimators are widely produced using Richardson extrapolation (RE) and variations of it. All these methods rely on the a priori existence of an asymptotic expansion of the error-such as a Taylor formula-and make no direct use of the PDE formulation. As a consequence, RE methods are extremely simple to implement. But in practice, meshes might not be fine enough to satisfy accurately the a priori convergence estimates that are asymptotic in nature. RE is unreliable or fairly unstable and sensitive to noisy data.