Error estimates for two-phase Stefan problems in several space variables. II: Nonlinear flux conditions

DOI10.1007/BF02575899zbMath0606.65085OpenAlexW2004159880MaRDI QIDQ1084846

Ricardo H. Nochetto

Publication date: 1985

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02575899

zbMATH Keywords

maximum principlerate of convergenceregularizationlinear finite elementimplicit Eulererror-estimatesnonlinear flux conditionstwo-phase Stefan problems

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Heat equation (35K05) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) 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

On the numerical approach to a two-phase Stefan problem with nonlinear flux, Error estimates for Euler forward scheme related to two-phase Stefan problems, Approximation of degenerate parabolic systems by nondegenerate elliptic and parabolic systems, Energy error estimates for a linear scheme to approximate nonlinear parabolic problems, Error estimates for multidimensional singular parabolic problems, Nonlinear diffusion in type-II superconductors, Newton method for reactive solute transport with equilibrium sorption in porous media, Error Estimates for a Nonlinear Degenerate Parabolic Problem, An Efficient Linear Scheme to Approximate Parabolic Free Boundary Problems: Error Estimates and Implementation, A characteristic Galerkin method with adaptive error control for the continuous casting problem, A Stable Extrapolation Method for Multidimensional Degenerate Parabolic Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• On the numerical approach to a two-phase Stefan problem with nonlinear flux
• Continuity of weak solutions to certain singular parabolic equations
• Approximation of nonlinear evolution systems
• Galerkin methods for parabolic equations with nonlinear boundary conditions
• Maximum principle and uniform convergence for the finite element method
• Transformation of dependent variables and the finite element solution of nonlinear evolution equations
• On the Existence of Weak-Solutions to an n-Dimensional Stefan Problem with Nonlinear Boundary Conditions
• An Enthalpty Formulation of the Stefan Problem
• A Numerical Solution of the Enthalpy Formulation of the Stefan Problem
• Maximum-Norm Interior Estimates for Ritz-Galerkin Methods
• Optimal L ∞ Estimates for the Finite Element Method on Irregular Meshes
• Interior Maximum Norm Estimates for Finite Element Methods
• 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
• The Stefan Problem in Several Space Variables