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.
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