Numerical simulations of nonlinear phase transitions—I. The isotropic case

DOI10.1016/0362-546X(88)90040-5zbMath0659.65131OpenAlexW2059350873MaRDI QIDQ3809205

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Publication date: 1988

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(88)90040-5

zbMATH Keywords

phase field modelfinite difference approximationssurface tensiondensitiesnumerical simulationfree boundary problemsdendritesisotropic casesupercoolingnonlinear instabilitiesnonlinear phase transitions

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Thermodynamics of continua (80A17) Free boundary problems for PDEs (35R35) Applications to the sciences (65Z05)

Related Items (5)

The numerical solution of a control problem governed by a phase filed model ⋮ Efficient computation of a sharp interface by spreading via phase field methods ⋮ Analysis of a fully discrete finite element method for the phase field model and approximation of its sharp interface limits ⋮ The numerical effect of an artificial term, solving a mixed partial differential equation ⋮ Computation of sharp phase boundaries by spreading: The planar and spherically symmetric cases

Cites Work

• On mixed finite element methods for first order elliptic systems
• Shape instabilities and pattern formation in solidification: A new method for numerical solution of the moving boundary problem
• The Numerical Analysis of a Phase Field Model in Moving Boundary Problems
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