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

  • 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.

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Metadaten
Document Type:Article
Author: Jafar Amani, Amir Saboor Bagherzadeh, Timon RabczukORCiDGND
DOI (Cite-Link):https://doi.org/10.1155/2014/721240Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170413-31181Cite-Link
Parent Title (English):Mathematical Problems in Engineering
Language:English
Date of Publication (online):2017/04/13
Year of first Publication:2014
Release Date:2017/04/13
Publishing Institution:Bauhaus-Universität Weimar
Institutes:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
Tag:MDLSM method
GND Keyword:Elastizität; Fehlerabschätzung
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften
BKL-Classification:54 Informatik / 54.80 Angewandte Informatik
56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)