scholarly journals A semi-implicit integration factor discontinuous Galerkin method for the non-linear heat equation

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1623-1628
Author(s):  
Rongpei Zhang ◽  
Xijun Yu ◽  
Mingjun Li ◽  
Zhen Wang
Keyword(s):  
Heat Conduction ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Second Order ◽  
Implicit Integration ◽  
Galerkin Scheme ◽  
Linear Heat ◽  
Discontinuous Galerkin Scheme ◽  
Non Linear

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.

SELECTION OF VISCOUS TERMS APPROXIMATION IN DISCONTINUOUS GALERKIN METHOD

2013 ◽  
Vol 44 (3) ◽  
pp. 327-354
Author(s):  
Aleksey Igorevich Troshin ◽  
Vladimir Viktorovich Vlasenko ◽  
Andrey Viktorovich Wolkov
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Selection Of
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