Abstract
We introduce and analyse a fully discrete approximation for a mathematical model for the solidification and liquidation of materials of negligible specific heat. The model is a two-sided Mullins–Sekerka problem. The discretization uses finite elements in space and an independent parameterization of the moving free boundary. We prove unconditional stability and exact volume conservation for the introduced scheme. Several numerical simulations, including for nearly crystalline surface energies, demonstrate the practicality and accuracy of the presented numerical method.
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- An assessment of solvers for algebraically stabilized discretizations of convection–diffusion–reaction equations
- A divergence-free finite element method for the Stokes problem with boundary correction
- A time-explicit weak Galerkin scheme for parabolic equations on polytopal partitions
- A structure preserving front tracking finite element method for the Mullins–Sekerka problem
Artikel in diesem Heft
- Frontmatter
- An assessment of solvers for algebraically stabilized discretizations of convection–diffusion–reaction equations
- A divergence-free finite element method for the Stokes problem with boundary correction
- A time-explicit weak Galerkin scheme for parabolic equations on polytopal partitions
- A structure preserving front tracking finite element method for the Mullins–Sekerka problem