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

Numerical Analysis;Numerical Analysis