Mesh scheme for a phase transition problem with time-fractional derivative
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Alexander Lapin
Abstract
The time-fractional phase transition problem, formulated in enthalpy form, is studied. This nonlinear problem with an unknown moving boundary includes, as an example, a mathematical model of one-phase Stefan problem with the latent heat accumulation memory. The posed problem is approximated by the backward Euler mesh scheme. The unique solvability of the mesh scheme is proved and a priori estimates for the solution are obtained. The properties of the mesh problem are studied, in particular, an estimate of movement rate for the mesh phase transition boundary is established. The proved estimate make it possible to localize the phase transition boundary and split the mesh scheme into the sum of a nonlinear problem of small algebraic dimension and a larger linear problem. This information can be used for further construction of efficient algorithms for implementing the mesh scheme. Several algorithms for implementing mesh scheme are briefly discussed.
Funding statement: This research was supported by the Russian Science Foundation, project No. 20-61-46017.
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Articles in the same Issue
- Frontmatter
- Variational data assimilation for a sea dynamics model
- Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients
- Mesh scheme for a phase transition problem with time-fractional derivative
- A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem
- Difference schemes for second-order ordinary differential equations with corrector and predictor properties
Articles in the same Issue
- Frontmatter
- Variational data assimilation for a sea dynamics model
- Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients
- Mesh scheme for a phase transition problem with time-fractional derivative
- A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem
- Difference schemes for second-order ordinary differential equations with corrector and predictor properties
