We consider an Eulerian-Lagrangian localized adjoint method (ELLAM) applied
to nonlinear model equations governing solute transport and sorption in porous
media. Solute transport in the aqueous phase is modeled by standard advection and
hydrodynamic dispersion processes, while sorption is modeled with a nonlinear local
equilibrium model. We present our implementation of finite volume ELLAM (FV-
ELLAM) and finite element (FE-ELLAM) discretizations to the reactive transport
model and evaluate their performance for several test problems containing self-
sharpening fronts
