Convergence of the approximate free boundary for the multidimensional one-phase Stefan problem

DOI10.1007/BF00277696zbMath0622.65126OpenAlexW2090406711MaRDI QIDQ1091094

Paola Pietra, Claudio Verdi

Publication date: 1986

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00277696

zbMATH Keywords

error estimateone-phase multidimensional Stefan problembackward-differences in timediscrete free boundarypiecewise-linear finite elements in space

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Thermodynamics of continua (80A17) Free boundary problems for PDEs (35R35) Applications to the sciences (65Z05)

Related Items

A note on the approximation of free boundaries by finite element methods, The variational inequality approach to the one-phase Stefan problem, Sharp \(L^{\infty}\)-error estimates for semilinear elliptic problems with free boundaries

Cites Work

• On finite element approximation in the \(L^{\infty}\)-norm of variational inequalities
• The regularity of free boundaries in higher dimensions
• Maximum principle and uniform convergence for the finite element method
• Convergence of the discrete free boundaries for finite element approximations
• The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem
• Uniform convergence of the horizontal line method for solutions and free boundaries in Stefan evolution inequalities
• ON THE CLASSICAL SOLUTION OF THE MULTIDIMENSIONAL STEFAN PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS
• A Convergence Estimate for an Approximation of a Parabolic Variational Inequality
• One-Dimensional Parabolic Free Boundary Problems
• The Stefan Problem in Several Space Variables
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
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