Adaptive discontinuous Galerkin methods for non-linear   diffusion-convection-reaction equations
  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. 
Murat Uzunca, B\"ulent Karas\"ozen, Murat Manguo\u{g}lu
math.NA