WIAS Preprint No. 871, (2003)

Transient conductive-radiative heat transfer: Discrete existence and uniqueness for a finite volume scheme*


  • Klein, Olaf
    ORCID: 0000-0002-4142-3603
  • Philip, Peter

2010 Mathematics Subject Classification

  • 45K05 65M99 35K05 35K55 65N22 47H10 80A20


  • Integro-partial differential equations, Finite volume method, Nonlinear parabolic PDEs, Integral operators, Nonlocal interface conditions, Diffuse-gray radiation, Maximum principle




This article presents a finite volume scheme for transient nonlinear heat transport equations coupled by nonlocal interface conditions modeling diffuse-gray radiation between the surfaces of (both open and closed) cavities. The model is considered in three space dimensions, modifications for the axisymmetric case are indicated. Proving a maximum principle as well as existence and uniqueness for roots to a class of discrete nonlinear operators that can be decomposed into a scalar-dependent sufficiently increasing part and a benign rest, we establish a discrete maximum principle for the finite volume scheme, yielding discrete L-L a priori bounds as well as a unique discrete solution to the finite volume scheme.

Appeared in

  • Mathematical Models and Methods in Applied Sciences, 15 (2005), 227-258

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