  In this work, we apply the adaptive discontinuous Galerkin (DGAFEM) method to
the convection dominated non-linear, quasi-stationary
diffusion-convection-reaction equations. We propose an efficient preconditioner
using a matrix reordering scheme to solve the sparse linear systems iteratively
arising from the discretized non-linear equations. Numerical examples
demonstrate effectiveness of the DGAFEM to damp the spurious oscillations and
resolve well the sharp layers occurring in convection dominated non-linear
equations.
