Error estimate and adaptive refinement in mixed discrete least squares meshless method

J. Amani, A. Saboor Bagherzadeh, Timon Rabczuk

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.

Original languageEnglish
Article number721240
JournalMathematical Problems in Engineering
Volume2014
DOIs
Publication statusPublished - 2014 Jan 1

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Adaptive Refinement
Meshless Method
Least Square Method
Error Estimates
Least Squares
Formulation
Refinement
Elasticity
Differential equations
Mixed Formulation
Robust Estimators
Elasticity Problem
Meshless
Error Estimator
Shape Function
Vertex of a graph
Fidelity
Convergence Rate
Governing equation
Differential equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Error estimate and adaptive refinement in mixed discrete least squares meshless method. / Amani, J.; Saboor Bagherzadeh, A.; Rabczuk, Timon.

In: Mathematical Problems in Engineering, Vol. 2014, 721240, 01.01.2014.

Research output: Contribution to journalArticle

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