Error analysis of a least squares pseudo-derivative moving least squares method.


  • Jhules Clack University of Cincinnati.
  • Donald A. French University of Cincinnati.
  • Mauricio Osorio Universidad Nacional de Colombia.


Pseudo-derivatives, Moving least square methods and error estimates


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.

Author Biographies

Jhules Clack, University of Cincinnati.

Department of Mathematical Sciences.

Donald A. French, University of Cincinnati.

Department of Mathematical Sciences.

Mauricio Osorio, Universidad Nacional de Colombia.

Escuela de Matemáticas.


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How to Cite

J. Clack, D. A. French, and M. Osorio, “Error analysis of a least squares pseudo-derivative moving least squares method.”, Proyecciones (Antofagasta, On line), vol. 36, no. 3, pp. 435-448, Oct. 2017.