A multilevel local mesh refinement with the PCD Method
Abstract
We propose in this contribution a successive local mesh refinement with the PCD method. The multilevel local refinement improves the accuracy and gives a better precision, locally and globally, with a lower computational costs particularly if the considered problem has an anomaly. Here we present how a successive local mesh refinement can be handled. We conclude by presenting numerical experiments to show the interest of a multilevel local mesh refinement for the 2D diffusion equation.
Downloads
References
R. Beauwens, Forgivale variational crimes, Lecture Notes in Computer Science, 2542 (2003), 3-11.
Z. Cai, J. Mandel and S.McCormick, The finite volume element method for diffusion equations on general triangulations, SIAM J. Numer. Anal. 28 (1991), 392-402.
Z. Cai and S. McCormick, On the accuracy of the finite volume element method for diffusion equations on composite grids, SIAM J. Numer. Anal. 27 (1990), 636-655.
R. E. Ewing, R. D. Lazarov and P. S. Vassilevski, Local refinement techniques for elliptic problems on cell-centred grid, I: Error analysis, Math. Comp. 56 (1991), 437-461.
A. Tahiri, The PCD method, Lecture Notes in Computer Science, 2542 (2003), 563-571.
A. Tahiri, Local mesh refinement with the PCD method, Adv. Dyn. Syst. Appl. 8(1) (2013), 124-136.
A. Tahiri, The PCD Method on Composite Grid, Bol. Soc. Paran. Mat. 34(2) (2016), 121-145.
A. Tahiri, The best strategy for local mesh refinement with the PCD method, Int. J. Dynamical Systems and Differential Equations, Vol. 8, Nos. 1/2, (2018), 19–32.
A. Tahiri, Numerical Computations of the PCD Method, Bol. Soc. Paran. Mat. 37(1) (2019), 39-54.
P. S. Vassilevski, S. I. Petrova and R. D. Lazarov, Finite difference schemes on triangular cell-centred grids with local refinement, SIAM J. Sci. Stat. Comput. 13 (1992), 1287-1313.
Copyright (c) 2020 Boletim da Sociedade Paranaense de Matemática

This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).