A finite element method for a single phase semilinear stefan problem in one space dimension

DOI10.1080/01630569108816422zbMath0757.65127OpenAlexW1988990320MaRDI QIDQ4009939

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Publication date: 27 September 1992

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569108816422

zbMATH Keywords

Galerkin methodfree boundaryquadratic nonlinearityOptimal error estimatesone-dimensional single phase semilinear Stefan problem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stefan problems, phase changes, etc. (80A22) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Free boundary problems for PDEs (35R35) Applications to the sciences (65Z05)

Related Items (8)

Error estimates for mixed finite element approximations to a linear Stefan problem. ⋮ Galerkin method for a Stefan-type problem in one space dimension ⋮ A discrete finite element Galerkin method for a unidimensional single-phase Stefan problem ⋮ Error analysis of finite element approximation of a Stefan problem with nonlinear free boundary condition ⋮ On superconvergence results and negative norm estimates for a unidimensional single phase stefan problem ⋮ Error analysis of a mixed finite element approximation of a linear Stefan problem. ⋮ Fully discrete mixed finite element method for a quasilinear Stefan problem with a forcing term in non-divergence form ⋮ Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber

Cites Work

• An \(H^ 1\)-Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form
• On Galerkin Methods in Semilinear Parabolic Problems
• Incomplete Iteration for Time-Stepping a Galerkin Method for a Quasilinear Parabolic Problem
• A Priori Error Estimates in H¹ and H² Norms for Galerkin Approximations to a Single-Phase Nonlinear Stefan Problem in One Space Dimension
• A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations

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