Adapting meshes and time-steps for phase change problems

Ricardo H. Nochetto; Alfred Schmidt; Claudio Verdi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1997)

  • Volume: 8, Issue: 4, page 273-292
  • ISSN: 1120-6330

Abstract

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We address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.

How to cite

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Nochetto, Ricardo H., Schmidt, Alfred, and Verdi, Claudio. "Adapting meshes and time-steps for phase change problems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.4 (1997): 273-292. <http://eudml.org/doc/244087>.

@article{Nochetto1997,
abstract = {We address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.},
author = {Nochetto, Ricardo H., Schmidt, Alfred, Verdi, Claudio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Degenerate parabolic equations; Stefan problem; Finite elements; A posteriori estimates; Adaptivity; degenerate parabolic equations; phase change problems; mesh refinement; stability; convergence; two-phase Stefan problem; adaptive finite element method; a posteriori error estimation},
language = {eng},
month = {12},
number = {4},
pages = {273-292},
publisher = {Accademia Nazionale dei Lincei},
title = {Adapting meshes and time-steps for phase change problems},
url = {http://eudml.org/doc/244087},
volume = {8},
year = {1997},
}

TY - JOUR
AU - Nochetto, Ricardo H.
AU - Schmidt, Alfred
AU - Verdi, Claudio
TI - Adapting meshes and time-steps for phase change problems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/12//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 4
SP - 273
EP - 292
AB - We address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.
LA - eng
KW - Degenerate parabolic equations; Stefan problem; Finite elements; A posteriori estimates; Adaptivity; degenerate parabolic equations; phase change problems; mesh refinement; stability; convergence; two-phase Stefan problem; adaptive finite element method; a posteriori error estimation
UR - http://eudml.org/doc/244087
ER -

References

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