Int. J. of Dynamical Systems and Differential Equations   »   2018 Vol.8, No.1/2

 

 

Title: The best strategy for local mesh refinement with the PCD method

 

Author: Ahmed Tahiri

 

Address: Department of Computer Science, Faculty of Sciences, University Mohammed I, Av Med 6, BP 717, 60000 Oujda, Morocco

 

Abstract: We propose in this contribution numerical tests for local mesh refinement with the PCD method. We investigate two rates of local mesh refinement: the ratio 2 and the ratio 3. First we introduce a local mesh refinement by subdividing the elements of the zone to be refined by the ratio 2 in each direction, i. e. each coarse element is subdivided by 4 fine elements. Second, we subdivide the elements of the zone to be refined by the ratio 3 in each direction, i. e. each coarse element is subdivided by 9 fine elements. Here we investigate some numerical experiments to show that the optimal local refinement rate is 2. This is in agreement with the regularity assumptions required for the proposed discretisation.

 

Keywords: boundary value problem; local mesh refinement; multilevel local refinement; optimal rate for local mesh refinement; PCD method; slave nodes.

 

DOI: 10.1504/IJDSDE.2018.10009156

 

Int. J. of Dynamical Systems and Differential Equations, 2018 Vol.8, No.1/2, pp.19 - 32

 

Submission date: 28 Sep 2016
Date of acceptance: 09 Feb 2017
Available online: 20 Nov 2017

 

 

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