Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations

Murat Uzunca; Bülent Karasözen; Murat Manguoğlu

doi:10.1016/j.compchemeng.2014.05.002

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arXiv · 1409.4313

Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations

Murat Uzunca·Bülent Karasözen·Murat Manguoğlu

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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.

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Murat Uzunca, Bülent Karasözen, Murat Manguoğlu. 2014-09-15. Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations. https://doi.org/10.1016/j.compchemeng.2014.05.002

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