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Finite element approximation of a Stefan problem with degenerate Joule heating

John W. Barrett, Robert Nürnberg (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a fully practical finite element approximation of the following degenerate system t ρ ( u ) - . ( α ( u ) u ) σ ( u ) | φ | 2 , . ( σ ( u ) φ ) = 0 subject to an initial condition on the temperature, u , and boundary conditions on both u and the electric potential, φ . In the above ρ ( u ) is the enthalpy incorporating the latent heat of melting, α ( u ) > 0 is the temperature dependent heat conductivity, and σ ( u ) 0 is the electrical conductivity. The latter is zero in the frozen zone, u 0 , which gives rise to the degeneracy in this Stefan system. In addition to showing stability...

Finite element approximation of a Stefan problem with degenerate Joule heating

John W. Barrett, Robert Nürnberg (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a fully practical finite element approximation of the following degenerate system t ρ ( u ) - . ( α ( u ) u ) σ ( u ) | φ | 2 , . ( σ ( u ) φ ) = 0 subject to an initial condition on the temperature, u, and boundary conditions on both u and the electric potential, ϕ. In the above p(u) is the enthalpy incorporating the latent heat of melting, α(u) > 0 is the temperature dependent heat conductivity, and σ(u) > 0 is the electrical conductivity. The latter is zero in the frozen zone, u ≤ 0, which gives rise to the degeneracy in this Stefan...

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