Three-field mixed hp-finite element method for the solution of the Guyer–Krumhansl heat conduction model

Tóth, Balázs (2023) Three-field mixed hp-finite element method for the solution of the Guyer–Krumhansl heat conduction model. INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 217. No-124663. ISSN 0017-9310

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Abstract

On the basis of numerous experimental studies the Guyer–Krumhansl heat conductivity model can be considered as one of the most promising theoretical models to simulate the low temperature processes and the thermal behavior of such complex structures as materials with inhomogeneities and interfaces, as well as porous materials. However, the classical ℎ-version finite element methods do not provide convergent and accurate results for the solution of the Guyer–Krumhansl heat conductivity model. In recent paper, a new three-field variational formulation is derived treating the temperature, the heat flow and its current density as independent variables. Both the temperature- and the heat flow boundary condition are weakly imposed, i.e., built in the variational form. Based on this variational background, a new, ℎ

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