A discontinuous Galerkin scheme for a stratigraphic model
Abdelaziz Taakili · 2006
Mots-cles : Pseudo-parabolic problem, degenerated problem, discontinuous Galerkin methods. In this talk, we study a mathematical problem arising from the modelling of maximal erosion rate in geological stratigraphic phenomena. The equation of this problems is nonlinear; the diffusion coefficient depends on the time-derivative of the unknown u and degenerates in order to take implicitly into account a global constraint on the time-derivative of u. This model has been initially developed by the Institut Francais du petrole and it takes into account sedimentation, transport, accumulation and erosion phenomena. Concerning physical and numerical description of these models, see in in R. Eymard and al. [6], [5]. The original mathematical aspect of this model is the imposition of a constraint on the timederivative of u. This leeds us to consider a class of conservation laws of degenerete pseudo-parabolic type that accurs in particular in the theory of elastic fluids in elasto-plastic porous media (see G. I. Barenblatt [3]) ∂tu−Div[λK(x)∇(u+ τ∂tu)] = 0, λ ∈ H(∂tu+ E), (1)