# Mathematical and numerical analysis of a stratigraphic model

Véronique Gervais; Roland Masson

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 38, Issue: 4, page 585-611
- ISSN: 0764-583X

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topGervais, Véronique, and Masson, Roland. "Mathematical and numerical analysis of a stratigraphic model." ESAIM: Mathematical Modelling and Numerical Analysis 38.4 (2010): 585-611. <http://eudml.org/doc/194229>.

@article{Gervais2010,

abstract = {
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 ci
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 ci 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.
},

author = {Gervais, Véronique, Masson, Roland},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Finite volume method; stratigraphic modelling; linear first order equations; convergence analysis; linear advection equation; unique weak solution; adjoint problem.},

language = {eng},

month = {3},

number = {4},

pages = {585-611},

publisher = {EDP Sciences},

title = {Mathematical and numerical analysis of a stratigraphic model},

url = {http://eudml.org/doc/194229},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Gervais, Véronique

AU - Masson, Roland

TI - Mathematical and numerical analysis of a stratigraphic model

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 4

SP - 585

EP - 611

AB -
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 ci
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 ci 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.

LA - eng

KW - Finite volume method; stratigraphic modelling; linear first order equations; convergence analysis; linear advection equation; unique weak solution; adjoint problem.

UR - http://eudml.org/doc/194229

ER -

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