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We propose an edge averaged finite element (EAFE) discretization to solve the Heat-PNP (Poisson-Nernst-Planck) equations approximately. Our method enforces positivity of computed charged density functions and temperature function. Also thermodynamic consistent discrete energy estimate which resembles second law system is prescribed. Numerical examples are provided.

The numerical simulation of all steps of the production of a steel workpiece is nowadays a widely used tool for understanding and optimization of such processes. The transformation of austenite into ferritic phases is an important feature of heat treatment of steel. Good models for the non-isothermal phase transition are a necessary prerequisite for various other modeling steps. We evaluate som...