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A SEMI-IMPLICIT INTEGRATION FACTOR DISCONTINUOUS GALERKIN METHOD FOR THE NON-LINEAR HEAT EQUATION

ABSTRACT
In this paper, a new discontinuous Galerkin method is employed to study the non-linear heat conduction equation with temperature dependent thermal conductivity. We present practical implementation of the new discontinuous Galerkin scheme with weighted flux averages. The second-order implicit integration factor for time discretization method is applied to the semi discrete form. We obtain the L2 stability of the discontinuous Galerkin scheme. Numerical examples show that the error estimates are of second order when linear element approximations are applied. The method is applied to the non-linear heat conduction equations with source term.
KEYWORDS
PAPER SUBMITTED: 2018-09-21
PAPER REVISED: 2018-11-05
PAPER ACCEPTED: 2018-12-27
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI180921232Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE 3, PAGES [1623 - 1628]
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© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence