Mathematical and numerical analysis of a stratigraphic model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 4, p. 585-611

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of $L$ lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness $h$, the $L$ surface concentrations ${c}_{i}^{s}$ in lithology $i$ of the sediments at the top of the basin, and the $L$ concentrations ${c}_{i}$ in lithology $i$ of the sediments inside the basin. For this simplified model, the sediment thickness decouples from the other unknowns and satisfies a linear parabolic equation. The remaining equations account for the mass conservation of the lithologies, and couple, for each lithology, a first order linear equation for ${c}_{i}^{s}$ with a linear advection equation for ${c}_{i}$ for which ${c}_{i}^{s}$ appears as an input boundary condition. For this coupled system, a weak formulation is introduced which is shown to have a unique solution. An implicit finite volume scheme is derived for which we show stability estimates and the convergence to the weak solution of the problem.

DOI : https://doi.org/10.1051/m2an:2004035
Classification:  35M10,  35L50,  35Q99,  65M12
Keywords: finite volume method, stratigraphic modelling, linear first order equations, convergence analysis, linear advection equation, unique weak solution, adjoint problem
@article{M2AN_2004__38_4_585_0,
author = {Gervais, V\'eronique and Masson, Roland},
title = {Mathematical and numerical analysis of a stratigraphic model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {38},
number = {4},
year = {2004},
pages = {585-611},
doi = {10.1051/m2an:2004035},
zbl = {1130.86315},
mrnumber = {2087725},
language = {en},
url = {http://www.numdam.org/item/M2AN_2004__38_4_585_0}
}

Gervais, Véronique; Masson, Roland. Mathematical and numerical analysis of a stratigraphic model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 4, pp. 585-611. doi : 10.1051/m2an:2004035. http://www.numdam.org/item/M2AN_2004__38_4_585_0/

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