The Accuracy of Least-Squares Approximation on Highly Stretched Meshes

The least-squares (LS) method is often used in computational aerodynamics to reconstruct a given function at certain points of a computational grid. In this paper we discuss the accuracy of the LS approximation on highly stretched meshes that. are inherent in computational aerodynamics. A new definition of a distant point in a LS reconstruction stencil will be given in order to explain the poor performance of the method in a boundary layer region. Namely, based on the concept of outliers widely used in the statistics, we demonstrate that; the definition of a distant point in a LS reconstruction stencil should take into account the solution properties and it cannot rely upon the geometric shape of the stencil only. Our approach is illustrated with numerical examples.