A multilevel local mesh refinement with the PCD Method

  • Ahmed Tahiri University Mohammed I

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

Download data is not yet available.

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.

Published
2020-10-07
Section
Articles