# Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time

Alexei Lozinski; Jacek Narski; Claudia Negulescu

- Volume: 48, Issue: 6, page 1701-1724
- ISSN: 0764-583X

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topLozinski, Alexei, Narski, Jacek, and 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 48.6 (2014): 1701-1724. <http://eudml.org/doc/273107>.

@article{Lozinski2014,

abstract = {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.},

author = {Lozinski, Alexei, Narski, Jacek, Negulescu, Claudia},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {anisotropic parabolic equation; ill-conditioned problem; singular perturbation model; limit model; asymptotic preserving scheme; stability; nonlinear heat equation; Runge-Kutta scheme},

language = {eng},

number = {6},

pages = {1701-1724},

publisher = {EDP-Sciences},

title = {Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time},

url = {http://eudml.org/doc/273107},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Lozinski, Alexei

AU - Narski, Jacek

AU - Negulescu, Claudia

TI - Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 6

SP - 1701

EP - 1724

AB - 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.

LA - eng

KW - anisotropic parabolic equation; ill-conditioned problem; singular perturbation model; limit model; asymptotic preserving scheme; stability; nonlinear heat equation; Runge-Kutta scheme

UR - http://eudml.org/doc/273107

ER -

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