Error analysis of a least squares pseudo-derivative moving least squares method.
French, Donald A.
Meshfree methods oﬀer the potential to relieve the scientist from the time consuming grid generation process especially in cases where localized mesh reﬁnement is desired. Moving least squares (MLS) methods are considered such a meshfree technique. The pseudo-derivative (PD) approach has been used in many papers to simplify the manipu- lations involved in MLS schemes. In this paper, we provide theoretical error estimates for a least squares implementation of an MLS/PD method with a stabilization mechanism. Some beginning computations suggest this stabilization leads to good matrix conditioning.