A discontinuous Galerkin method for a model arising from stratigraphy

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.