Geodesic
Finite element solution of a stationary heat conduction equation with the radiation boundary condition
Applications of Mathematics, Tome 38 (1993) no. 1, pp. 67-79.

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In this paper we present a weak formulation of a two-dimensional stationary heat conduction problem with the radiation boundary condition. The problem can be described by an operator which is monotone on the convex set of admissible functions. The relation between classical and weak solutions as well as the convergence of the finite element method to the weak solution in the norm of the Sobolev space $H^1 (\Omega)$ are examined.
DOI : 10.21136/AM.1993.104535
Classification : 35J25, 65N30, 80A20
Keywords: heat conduction; heat radiation; finite elements; Stefan-Boltzmann boundary condition; stationary heat conduction 
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     title = {Finite element solution of a stationary heat conduction equation with the radiation boundary condition},
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Milka, Zdeněk. Finite element solution of a stationary heat conduction equation with the radiation boundary condition. Applications of Mathematics, Tome 38 (1993) no. 1, pp. 67-79. doi : 10.21136/AM.1993.104535. http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104535/

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