A linear extrapolation method for a general phase relaxation problem

Xun Jiang

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1996)

  • Volume: 7, Issue: 3, page 169-179
  • ISSN: 1120-6330

Abstract

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This paper examines a linear extrapolation time-discretization of a 2 ⁢ D phase relaxation model with temperature dependent convection and reaction. The model consists of a diffusion-advection PDE for temperature and an ODE with double obstacle ± 1 for phase variable. Under a stability constraint, this scheme is shown to converge with optimal orders O ⁢ τ ⁢ log ⁡ τ 1 / 2 for temperature and enthalpy, and O ⁢ τ 1 / 2 ⁢ log ⁡ τ 1 / 2 for heat flux as time-step τ ↓ 0 .

How to cite

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Jiang, Xun. "A linear extrapolation method for a general phase relaxation problem." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.3 (1996): 169-179. <http://eudml.org/doc/244327>.

@article{Jiang1996,
abstract = {This paper examines a linear extrapolation time-discretization of a \( 2D \) phase relaxation model with temperature dependent convection and reaction. The model consists of a diffusion-advection PDE for temperature and an ODE with double obstacle \( \pm 1 \) for phase variable. Under a stability constraint, this scheme is shown to converge with optimal orders \( \mathcal\{O\} (\tau | \log \tau |^\{1/2\}) \) for temperature and enthalpy, and \( \mathcal\{O\} (\tau^\{1/2\} | \log \tau |^\{1/2\}) \) for heat flux as time-step \( \tau \downarrow 0 \).},
author = {Jiang, Xun},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Phase relaxation; Stefan problem; Error estimate; Semi-implicit; Extrapolation; error estimate; semi-implicit; extrapolation; time-discretization; 2D phase relaxation model; diffusion-advection},
language = {eng},
month = {12},
number = {3},
pages = {169-179},
publisher = {Accademia Nazionale dei Lincei},
title = {A linear extrapolation method for a general phase relaxation problem},
url = {http://eudml.org/doc/244327},
volume = {7},
year = {1996},
}

TY - JOUR
AU - Jiang, Xun
TI - A linear extrapolation method for a general phase relaxation problem
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/12//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 3
SP - 169
EP - 179
AB - This paper examines a linear extrapolation time-discretization of a \( 2D \) phase relaxation model with temperature dependent convection and reaction. The model consists of a diffusion-advection PDE for temperature and an ODE with double obstacle \( \pm 1 \) for phase variable. Under a stability constraint, this scheme is shown to converge with optimal orders \( \mathcal{O} (\tau | \log \tau |^{1/2}) \) for temperature and enthalpy, and \( \mathcal{O} (\tau^{1/2} | \log \tau |^{1/2}) \) for heat flux as time-step \( \tau \downarrow 0 \).
LA - eng
KW - Phase relaxation; Stefan problem; Error estimate; Semi-implicit; Extrapolation; error estimate; semi-implicit; extrapolation; time-discretization; 2D phase relaxation model; diffusion-advection
UR - http://eudml.org/doc/244327
ER -

References

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  11. VERDI, C. - VISINTIN, A., Error estimates for a semi-explicit numerical scheme for Stefan-type problems. Numer. Math., 52, 1988, 165-185. Zbl0617.65125MR923709DOI10.1007/BF01398688
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