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.

A nonlinearity lagging method for non-steady diffusion equations with nonlinear convection terms / Mezzadri, F.; Galligani, E.. - In: ADVANCES IN COMPUTATIONAL MATHEMATICS. - ISSN 1019-7168. - 45:3(2019), pp. 1185-1220. [10.1007/s10444-018-9652-2]

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

#### 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.
##### Scheda breve Scheda completa Scheda completa (DC)
2019
45
3
1185
1220
A nonlinearity lagging method for non-steady diffusion equations with nonlinear convection terms / Mezzadri, F.; Galligani, E.. - In: ADVANCES IN COMPUTATIONAL MATHEMATICS. - ISSN 1019-7168. - 45:3(2019), pp. 1185-1220. [10.1007/s10444-018-9652-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1188533`