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Advances in Computational Mathematics

, Volume 45, Issue 3, pp 1185–1220 | Cite as

A nonlinearity lagging method for non-steady diffusion equations with nonlinear convection terms

  • Francesco MezzadriEmail author
  • Emanuele Galligani
Article
  • 52 Downloads

Abstract

We analyze an iterative procedure for solving nonlinear algebraic systems arising from the discretization of nonlinear, non-steady reaction-convection-diffusion equations with non-constant (and, in general, nonlinear) velocity terms. The basic idea underlying the procedure consists in lagging the diffusion and the velocity terms of the discretized system, which is thus partly linearized. After analyzing the discretized system and proving some results on the monotonicity of the operators and on the uniqueness of the solution, we prove sufficient conditions that ensure the convergence of this lagged method. We also describe the inner iteration and show how the weakly nonlinear systems arising at each lagged iteration can be solved efficiently. Finally, we analyze numerically the entire solution process by several numerical experiments.

Keywords

Nonlinear diffusion equations Lagged diffusivity method Finite differences 

Mathematics Subject Classification (2010)

65H10 65M06 65M22 

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Notes

Acknowledgments

The authors desire to thank the anonymous referee for the helpful comments and remarks.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Engineering “Enzo Ferrari”University of Modena and Reggio EmiliaModenaItaly

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