scholarly journals Collocated discrete least-squares (CDLS) meshless method: error estimate and adaptive refinement

2008 ◽  
Vol 56 (10) ◽  
Author(s):  
M. H. Afshar ◽  
M. Lashckarbolok
Keyword(s):  
Error Estimate ◽  
Least Squares ◽  
Meshless Method ◽  
Adaptive Refinement ◽  
Method Error

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

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
J. Amani ◽  
A. Saboor Bagherzadeh ◽  
T. Rabczuk
Keyword(s):  
Convergence Rate ◽  
Error Estimate ◽  
Least Squares ◽  
Meshless Method ◽  
Least Square ◽  
Adaptive Refinement ◽  
Error Estimator ◽  
Shape Functions ◽  
Numerical Errors ◽  
Elasticity Problems

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.

Solution for fractional distributed optimal control problem by hybrid meshless method

2016 ◽  
Vol 24 (11) ◽  
pp. 2149-2164 ◽  
Author(s):  
Majid Darehmiraki ◽  
Mohammad Hadi Farahi ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Least Squares ◽  
Meshless Method ◽  
Basis Functions ◽  
Moving Least Squares ◽  
Distributed Optimal Control

We use a hybrid local meshless method to solve the distributed optimal control problem of a system governed by parabolic partial differential equations with Caputo fractional time derivatives of order α ∈ (0, 1]. The presented meshless method is based on the linear combination of moving least squares and radial basis functions in the same compact support, this method will change between interpolation and approximation. The aim of this paper is to solve the system of coupled fractional partial differential equations, with necessary and sufficient conditions, for fractional distributed optimal control problems using a combination of moving least squares and radial basis functions. To keep matters simple, the problem has been considered in the one-dimensional case, however the techniques can be employed for both the two- and three-dimensional cases. Several test problems are employed and results of numerical experiments are presented. The obtained results confirm the acceptable accuracy of the proposed method.

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