Variational approach to the construction of finitedifference schemes for the heat equation on curvilinear networks
Abstract
In the present paper, it is proposed to construct difference schemes, written in terms of heat fluxes, for the heat equation, using curvilinear networks. The construction of the schemes is based on a variational principle for the heat fluxes, formulated in this paper. The operators of the difference schemes retain such important properties as selfadjointness and the property of having fixed sign. The schemes are stable and provide secondorder approximation with respect to space and firstorder approximation with respect to time.
 Publication:

Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki
 Pub Date:
 April 1980
 Bibcode:
 1980ZVMMF..20..401K
 Keywords:

 Conductive Heat Transfer;
 Finite Difference Theory;
 Thermal Conductivity;
 Thermodynamics;
 Variational Principles;
 Approximation;
 Convergence;
 Integral Equations;
 Operators (Mathematics);
 Fluid Mechanics and Heat Transfer