The paper describes a formally strictly convergent algorithm for solving a class of elliptic problems with nonlinear and nonlocal boundary conditions, which arise in modeling of the steady-state conductive-radiative heat transfer processes. The proposed algorithm has two levels of iterations, where inner iterations by means of the damped Newton method solve an appropriate elliptic problem with nonlinear, but local boundary conditions, and outer iterations deal with nonlocal terms in boundary conditions.
Birgelis, K., & Raitums, U. (2012). Strictly convergent algorithm for an elliptic equation with nonlocal and nonlinear boundary conditions. Mathematical Modelling and Analysis, 17(1), 128-139. https://doi.org/10.3846/13926292.2012.647100
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