Error Estimates in Sobolev Spaces for Moving Least Square Approximations

MARÍA G. ARMENTANO

SIAM JOURNAL ON NUMERICAL ANALYSIS

SIAM PUBLICATIONS

Año: 2001 vol. 39 p. 38 - 51

0036-1429

The aim of this paper is to obtain error estimates for moving least square (MLS)approximations in RN. We prove that, under appropriate hypotheses on the weight function andthe distribution of points, the method produces optimal order error estimates in L1 and L2 forthe approximations of the function and its first derivatives. These estimates are important in theanalysis of Galerkin approximations based on the MLS method. In particular, our results provideerror estimates, optimal in order and regularity, for second order coercive problems.