Mathematical and numerical analysis of a stratigraphic model
ESAIM: Modélisation mathématique et analyse numérique, Volume 38 (2004) no. 4, pp. 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: 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
     author = {Gervais, V\'eronique and Masson, Roland},
     title = {Mathematical and numerical analysis of a stratigraphic model},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {585--611},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {4},
     year = {2004},
     doi = {10.1051/m2an:2004035},
     mrnumber = {2087725},
     zbl = {1130.86315},
     language = {en},
     url = {}
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Gervais, Véronique; Masson, Roland. Mathematical and numerical analysis of a stratigraphic model. ESAIM: Modélisation mathématique et analyse numérique, Volume 38 (2004) no. 4, pp. 585-611. doi : 10.1051/m2an:2004035.

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