Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations
Numerical Analysis
2014-09-16 v1
Abstract
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.
Cite
@article{arxiv.1409.4313,
title = {Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations},
author = {Murat Uzunca and Bülent Karasözen and Murat Manguoğlu},
journal= {arXiv preprint arXiv:1409.4313},
year = {2014}
}