Lagrange{galerkin Approximation for Advection{dominated Contaminant Transport with Nonlinear Equilibrium or Non{equilibrium Adsorption

An extension of the Lagrange{Galerkin approach is developed for advection-dominated problems with nonlinear adsorption, either being in equilibrium or in non{equilibrium, possibly with isotherms of the Freundlich type. The scheme should be feasable also for the hyperbolic limit case. The basic problems to deal with are the possibility of non{unique characteristics due to the nonlinear isotherms and the incorporation of the time{dependent non{ equilibrium adsorption kinetics, avoiding a strong restriction on the CFL{number. The one{dimensional scheme derived is able to handle shock solutions. In the non{equilibrium case a more severe restriction on the timestep has to be regarded.