Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations
This work addresses the challenge of solving convection-dominated non-linear PDEs, but the results are incremental as they demonstrate known advantages of DG methods on a specific problem class.
The authors applied adaptive discontinuous Galerkin methods to non-linear diffusion-convection-reaction equations and proposed an efficient preconditioner for iterative solvers. Numerical examples showed effectiveness in damping spurious oscillations and resolving sharp layers.
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.