×

A hybrid flux model for heat conduction problems. (English) Zbl 0966.80002

Summary: A hybrid method of solution for the linear problem of heat conduction in a body is presented. The variational support is a two-field functional whose arguments are heat flux, which meets a priori inner thermal equilibrium, and temperature on the boundary of the body. The stationary conditions of the functional are Fourier’s law and the prescribed boundary conditions. This variational framework allows to develop a finite element model that exhibits good accuracy, especially in the presence of geometry irregularities in a mesh.

MSC:

80A17 Thermodynamics of continua
74A15 Thermodynamics in solid mechanics
80M25 Other numerical methods (thermodynamics) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Heat Conduction. Wiley: Chichester, 1993.
[2] The Finite Element Method, vol. 1. McGraw-Hill: London, 1989.
[3] The Finite Element Method in Heat Transfer Analysis. Wiley: Chichester, 1996.
[4] Heat Conduction. CISM-Centro Internazionale di Scienze Meccaniche: Udine, 1972.
[5] Fraeijs de Veubeke, International Journal for Numerical Methods in Engineering 5 pp 65– (1972) · Zbl 0251.65061
[6] Mixed and Hybrid Finite Element Methods. Springer: New York, 1991. · Zbl 0788.73002
[7] A mixed finite element method for second order elliptic problems. In Mathematical Aspects of Finite Element Method, Lectures Notes in Mathematics, vol. 606. Springer: Berlin, 1977; 292-315.
[8] Mohan, Numerical Heat Transfer, Part B 30 pp 117– (1996)
[9] Mixed and irreducible formulations in finite element analysis. In Hybrid and Mixed Finite Element Methods, et al. (eds). Wiley: NewYork, 1983; 405-431.
[10] Hybrid models, In Numerical and Computer Methods in Structural Mechanics, et al. (eds). Academic Press: NewYork, 1973; 50-80.
[11] Unified finite element transient analysis formulations for interdisciplinary thermal structural problems. In Numerical Methods in Thermal problems, vol. VII, part 2, et al. (eds). 1991; 1238-1251.
[12] Un modello ibrido ai flussi in conduzione del calore. Proceedings of XIII Congresso Nazionale AIMETA, vol. 3, Siena, Italy, 1997; 219-226.
[13] MacNeal, Finite Elements Analysis Design 1 pp 3– (1985)
[14] An Introduction to the Finite Element Method. McGraw-Hill: New York, 1993.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.