Commun. Comput. Phys., 8 (2010), pp. 642-662.


The Monotone Robin-Robin Domain Decomposition Methods for the Elliptic Problems with Stefan-Boltzmann Conditions

Wenbin Chen 1*, Jin Cheng 2, Masahiro Yamamoto 3, Weili Zhang 2

1 School of Mathematical Sciences and Key Laboratory of Computational Physics (MOE), Fudan University, Shanghai, 200433, China; and Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, 200433, China.
2 School of Mathematical Sciences and Key Laboratory of Computational Physics (MOE), Fudan University, Shanghai, 200433, China.
3 Department of Mathematical Sciences, University of Tokyo, Tokyo, 153-8914, Japan.

Received 16 June 2009; Accepted (in revised version) 3 December 2009
Available online 15 April 2010
doi:10.4208/cicp.150609.031209a

Abstract

This paper is concerned with the elliptic problems with nonlinear Stefan-Boltzmann boundary condition. By combining with the monotone method, the Robin-Robin domain decomposition methods are proposed to decouple the nonlinear interface and boundary condition. The monotone properties are verified for both the multiplicative and the additive domain decomposition methods. The numerical results confirm the theoretical analysis.

AMS subject classifications: 35J65, 65N55

Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Nonlinear Stefan-Boltzmann condition, monotone methods, Robin-Robin domain decomposition method.

*Corresponding author.
Email: wbchen@fudan.edu.cn (W. Chen), jcheng@fudan.edu.cn (J. Cheng), myama@ms.u-tokyo.ac.jp (M. Yamamoto), zhangwl@fudan.edu.cn (W. Zhang)
 

The Global Science Journal