A discontinuous Galerkin method for a model arising from stratigraphy

R. Becker (1) , Guy Vallet (1) , A. Taakili

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We investigate a mathematical problem arising from the modeling of maximal erosion rates in geological stratigraphy. A global constraint on ∂tu, the time-derivative of the solution, is the main feature of this model. This leads to a nonlinear pseudoparabolic equation with a diffusion coefficient which is a nonlinear function of ∂tu. Moreover, the problem degenerates in order to take implicitly into account the constraint. In this paper, we develop a numerical scheme based on the discontinuous Galerkin finite element method (DgFem) for its numerical approximation. With a particular choice of the flux at the interface, we prove that the constraint is implicitly satisfied by using piecewise constant approximation. This is confirmed by some numerical experiments. © 2013 IMACS.

Mots clés: Constraint; Discontinuous Galerkin finite-element method; Discontinuous Galerkin methods; Nonlinear pseudoparabolic equations; Numerical approximations; Numerical experiments; Piecewise-constant approximation; Pseudoparabolic; Diffusion; Nonlinear equations; Stratigraphy; Galerkin methods

Domaines: Analyse numérique [math.NA]

R. Becker, Guy Vallet, A. Taakili. A discontinuous Galerkin method for a model arising from stratigraphy. Applied Numerical Mathematics, 2014, 78, pp.68-79. ⟨10.1016/j.apnum.2013.06.010⟩. ⟨hal-00993680⟩