On the numerical approach to a two-phase Stefan problem with nonlinear flux

DOI10.1007/BF02600382zbMath0612.65084MaRDI QIDQ1088391

Claudio Verdi

Publication date: 1985

Published in: Calcolo (Search for Journal in Brave)

zbMATH Keywords

convergencenumerical exampletwo-phase Stefan problemGauss-SeidelChernoff formulaCrandall-Liggett formula

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Initial-boundary value problems for second-order parabolic equations (35K20) Thermodynamics of continua (80A17) Free boundary problems for PDEs (35R35) Applications to the sciences (65Z05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Cites Work

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• Continuity of the temperature in the two-phase Stefan problem
• A generalized Stefan problem in several space variables
• Error estimates for two-phase Stefan problems in several space variables. I: Linear boundary conditions
• Error estimates for two-phase Stefan problems in several space variables. II: Nonlinear flux conditions
• The moving finite element method: Applications to general partial differential equations with multiple large gradients
• Continuity of weak solutions to certain singular parabolic equations
• Approximation of nonlinear evolution systems
• Semi-linear second-order elliptic equations in \(L^1\)
• Convergence and approximation of semigroups of nonlinear operators in Banach spaces
• Galerkin methods for parabolic equations with nonlinear boundary conditions
• A Modified Finite Difference Scheme for the Stefan Problem
• A Finite-element Front-tracking Enthalpy Method for Stefan Problems
• On the Existence of Weak-Solutions to an n-Dimensional Stefan Problem with Nonlinear Boundary Conditions
• An Error Estimate for Changing the Stefan Problem
• An Enthalpty Formulation of the Stefan Problem
• A Numerical Solution of the Enthalpy Formulation of the Stefan Problem
• Some results on the multi-phase stefan problem
• A Galerkin Method for Nonlinear Parabolic Equations with Nonlinear Boundary Conditions
• Error Estimates for the Multidimensional Two-Phase Stefan Problem
• Analyse Numerique d’un Probleme de Stefan a Deux Phases Par une Methode d’Elements Finis
• The Stefan Problem in Several Space Variables
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
• Multidimensional Stefan Problems
• Nonlinear evolution equations in Banach spaces