An inverse problem for the one-phase Stefan problem with varying melting temperature

2025/12/16 by Marc Dambrine, Helmut Harbrecht, Dambrine, Marc +1
Engineering · Mathematics · Materials Science · #Phase Change Materials Research #Numerical methods in inverse problems #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2512.13975

Abstract

The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies over time. This occurs in practice, for example, when the pressure in the external space changes in time. In the corresponding backward problem, we then reconstruct the time-dependent melting temperature from the knowledge of the evolving geometry. We develop respective numerical algorithms using a moving mesh finite element method and provide numerical simulations.

Citations

• Boundary integral operators for the heat equation in time-dependent domains
• Global stability and decay for the classical Stefan problem
• Well-posedness for the classical Stefan problem and the zero surface tension limit
• L 2 Solvability and Representation by Caloric Layer Potentials in Time- Varying Domains
• An algorithm for the machine calculation of complex Fourier series
• A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

Related

• Recovering the initial condition in the One-Phase Stefan problem
• Analytical and numerical solutions to the three-phase Stefan problem with simultaneous occurrences of melting, solidification, boiling, and condensation phenomena
• The Stefan problem with variable thermophysical properties and phase\n change temperature
• Global stability and decay for the classical Stefan problem
• Input-to-State Stability for the Control of Stefan Problem with Respect to Heat Loss