Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 6, p. 1701-1724
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This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is second-order accurate in both, temporal and spacial variables. The discretization in time is done using an L-stable Runge-Kutta scheme. The convergence of the method is shown to be independent of the anisotropy parameter , and this for fixed coarse Cartesian grids and for variable anisotropy directions. The context of this work are magnetically confined fusion plasmas.

DOI : https://doi.org/10.1051/m2an/2014016
Classification:  65N30,  65Z05,  35K20
Keywords: anisotropic parabolic equation, ill-conditioned problem, singular perturbation model, limit model, asymptotic preserving scheme
@article{M2AN_2014__48_6_1701_0,
     author = {Lozinski, Alexei and Narski, Jacek and Negulescu, Claudia},
     title = {Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {6},
     year = {2014},
     pages = {1701-1724},
     doi = {10.1051/m2an/2014016},
     mrnumber = {3264370},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_6_1701_0}
}
Lozinski, Alexei; Narski, Jacek; Negulescu, Claudia. Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 6, pp. 1701-1724. doi : 10.1051/m2an/2014016. http://www.numdam.org/item/M2AN_2014__48_6_1701_0/

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