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 meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

1. Briefly summarize the paper's contributions. Does it address a new problem? Does it present a new approach? Does it show new types of results?  [AS] This paper presents a new point set surface representation by combining implicit moving least squares (IMLS) with robust statistics. In particular, they explicitly derive IMLS in the local kernel regression (LKR) framework, forming the basis of...

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than whe...