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Mathematical Problems in Engineering
Volume 2014, Article ID 721240, 16 pages
Research Article

Error Estimate and Adaptive Refinement in Mixed Discrete Least Squares Meshless Method

1Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstrasse 15, 99423 Weimar, Germany
2School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, Republic of Korea

Received 3 October 2013; Accepted 29 December 2013; Published 16 February 2014

Academic Editor: Stephane P. A. Bordas

Copyright © 2014 J. Amani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.