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Volume 1, Issue 1
Numerical Approximation of a Nonlinear 3D Heat Radiation Problem

Liping Liu, Min Huang, Kewei Yuan & Michal Křížek

Adv. Appl. Math. Mech., 1 (2009), pp. 125-139.

Published online: 2009-01

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  • Abstract

In this paper, we are concerned with the numerical approximation of a steady-state heat radiation problem with a nonlinear Stefan-Boltzmann boundary condition in $\mathbb{R}^3$. We first derive an equivalent minimization problem and then present a finite element analysis to the solution of such a minimization problem. Moreover, we apply the Newton iterative method for solving the nonlinear equation resulting from the minimization problem. A numerical example is given to illustrate theoretical results.

  • Keywords

Heat radiation problem, Stefan-Boltzmann condition, Newton iterative method.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-1-125, author = {Liu , LipingHuang , MinYuan , Kewei and Křížek , Michal}, title = {Numerical Approximation of a Nonlinear 3D Heat Radiation Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {1}, pages = {125--139}, abstract = {

In this paper, we are concerned with the numerical approximation of a steady-state heat radiation problem with a nonlinear Stefan-Boltzmann boundary condition in $\mathbb{R}^3$. We first derive an equivalent minimization problem and then present a finite element analysis to the solution of such a minimization problem. Moreover, we apply the Newton iterative method for solving the nonlinear equation resulting from the minimization problem. A numerical example is given to illustrate theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/212.html} }
TY - JOUR T1 - Numerical Approximation of a Nonlinear 3D Heat Radiation Problem AU - Liu , Liping AU - Huang , Min AU - Yuan , Kewei AU - Křížek , Michal JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 125 EP - 139 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/212.html KW - Heat radiation problem, Stefan-Boltzmann condition, Newton iterative method. AB -

In this paper, we are concerned with the numerical approximation of a steady-state heat radiation problem with a nonlinear Stefan-Boltzmann boundary condition in $\mathbb{R}^3$. We first derive an equivalent minimization problem and then present a finite element analysis to the solution of such a minimization problem. Moreover, we apply the Newton iterative method for solving the nonlinear equation resulting from the minimization problem. A numerical example is given to illustrate theoretical results.

Liu , LipingHuang , MinYuan , Kewei and Křížek , Michal. (2009). Numerical Approximation of a Nonlinear 3D Heat Radiation Problem. Advances in Applied Mathematics and Mechanics. 1 (1). 125-139. doi:
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