This paper provides the error estimates for generalized moving least squares (GMLS) derivatives approximations of a Sobolev function in L norms and extends them for local weak forms of DMLPG methods. Sometimes they are called diffuse or uncertain derivatives, but precisely they are direct approximants of exact derivatives which possess the optimal rates of convergence. GMLS derivatives approxim...

For the structural systems with both epistemic and aleatory uncertainties, in order to analyze the effect of the epistemic uncertainty on the safety of the systems, a variance based importance measure of failure probability is constructed. Due to the large computational cost of the proposed measure, a novel moving least squares (MLS) based method is employed. By fitting the relationship of para...

A method for moving least squares interpolation and differentiation is presented in the framework of orthogonal polynomials on discrete points. This yields a robust and efficient method which can avoid singularities and breakdowns in the moving least squares method caused by particular configurations of nodes in the system. The method is tested by applying it to the estimation of first and seco...

Developing suitable interpolation methods to simulate dynamic motions of continuous materials such as fluids is an important problem. In this paper, we propose a novel method to enforce the divergence condition to the interpolated velocity field by moving least squares, by means of the diffusive derivatives and moving divergence constraints that allow the practical use and easy implementation. ...