Error bounds for GMLS derivatives approximations of Sobolev functions

Abstract

This paper provides the error estimates for generalized moving least squares (GMLS) derivatives approximations of a Sobolev function in Lp 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 approximations are different from the standard derivatives of MLS approximation. While they are much easier to evaluate at considerably lower cost, in this paper the same orders of convergence with comparison to the standard derivatives are obtained for them. © 2015 Elsevier B.V. All rights reserved.