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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 = {Liping and Liu and and 20647 and and Liping Liu and Min and Huang and and 20648 and and Min Huang and Kewei and Yuan and and 20649 and and Kewei Yuan and Michal and Křížek and and 20650 and and Michal Křížek}, 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.

Liping Liu, Min Huang, Kewei Yuan & Michal Křížek. (1970). Numerical Approximation of a Nonlinear 3D Heat Radiation Problem. Advances in Applied Mathematics and Mechanics. 1 (1). 125-139. doi:
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