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On the maximum and comparison principles for a steady‐state nonlinear heat conduction problem
Author(s) -
Křížek M.,
Liu L.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310054
Subject(s) - thermal conduction , maximum principle , nonlinear system , mathematics , boundary value problem , mathematical analysis , dirichlet boundary condition , dirichlet distribution , anisotropy , steady state (chemistry) , physics , thermodynamics , mathematical optimization , chemistry , quantum mechanics , optimal control
We examine a Dirichlet boundary value problem of elliptic type which serves as a model for a stationary heat conduction in nonlinear, inhomogeneous, and anisotropic media. We prove a comparison principle and obtain the maximum principle as a direct consequence. We also show that the standard trilinear finite elements do not preserve a discrete maximum principle.