On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems

Mezzadri, Francesco; Galligani, Emanuele

doi:10.3390/a10030088

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Discretization Of the Convective Term And Convection-dominat...1

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2018

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“…Thus, we here consider this alternative discretization in order to show numerically its behavior and to provide an useful framework for convection-dominated problems. Further information on this case (referred to the case of constant velocity term) can be also found in [10].…”

Section: Discretization Of the Convective Term And Convection-dominat...mentioning

confidence: 99%

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

Mezzadri

Galligani

2018

Adv Comput Math

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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.

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Section: Discretization Of the Convective Term And Convection-dominat...mentioning

confidence: 99%

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

Mezzadri

Galligani

2018

Adv Comput Math

Self Cite

View full text Add to dashboard Cite

show abstract

On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems

Cited by 1 publication

References 20 publications

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

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

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