Artículo
Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model
Autor/es | Guillén González, Francisco Manuel
Gutiérrez Santacreu, Juan Vicente |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2009 |
Fecha de depósito | 2016-11-10 |
Publicado en |
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Resumen | We analyze two numerical schemes of Euler type in time and C0 finite-element type with P1-approximation in space for solving a phase-field model of a binary alloy with thermal properties. This model is written as a highly ... We analyze two numerical schemes of Euler type in time and C0 finite-element type with P1-approximation in space for solving a phase-field model of a binary alloy with thermal properties. This model is written as a highly non-linear parabolic system with three unknowns: phase-field, solute concentration and temperature, where the diffusion for the temperature and solute concentration may degenerate. The first scheme is nonlinear, unconditionally stable and convergent. The other scheme is linear but conditionally stable and convergent. A maximum principle is avoided in both schemes, using a truncation operator on the L2 projection onto the P0 finite element for the discrete concentration. In addition, for the model when the heat conductivity and solute diffusion coefficients are constants, optimal error estimates for both schemes are shown based on stability estimates. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España |
Identificador del proyecto | MTM2006-07932
117/06 |
Cita | Guillén González, F.M. y Gutiérrez Santacreu, J.V. (2009). Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model. ESAIM: Mathematical Modelling and Numerical Analysis, 43 (3), 563-589. |
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