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

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.