The second order projection method in time for the time-dependent natural convection problem

Yanxia Qian; Tong Zhang

Applications of Mathematics (2016)

  • Volume: 61, Issue: 3, page 299-315
  • ISSN: 0862-7940

Abstract

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We consider the second-order projection schemes for the time-dependent natural convection problem. By the projection method, the natural convection problem is decoupled into two linear subproblems, and each subproblem is solved more easily than the original one. The error analysis is accomplished by interpreting the second-order time discretization of a perturbed system which approximates the time-dependent natural convection problem, and the rigorous error analysis of the projection schemes is presented. Our main results of the second order projection schemes for the time-dependent natural convection problem are that the convergence for the velocity and temperature are strongly second order in time while that for the pressure is strongly first order in time.

How to cite

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Qian, Yanxia, and Zhang, Tong. "The second order projection method in time for the time-dependent natural convection problem." Applications of Mathematics 61.3 (2016): 299-315. <http://eudml.org/doc/276985>.

@article{Qian2016,
abstract = {We consider the second-order projection schemes for the time-dependent natural convection problem. By the projection method, the natural convection problem is decoupled into two linear subproblems, and each subproblem is solved more easily than the original one. The error analysis is accomplished by interpreting the second-order time discretization of a perturbed system which approximates the time-dependent natural convection problem, and the rigorous error analysis of the projection schemes is presented. Our main results of the second order projection schemes for the time-dependent natural convection problem are that the convergence for the velocity and temperature are strongly second order in time while that for the pressure is strongly first order in time.},
author = {Qian, Yanxia, Zhang, Tong},
journal = {Applications of Mathematics},
keywords = {natural convection problem; projection method; stability; convergence; natural convection problem; projection method; stability; convergence},
language = {eng},
number = {3},
pages = {299-315},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The second order projection method in time for the time-dependent natural convection problem},
url = {http://eudml.org/doc/276985},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Qian, Yanxia
AU - Zhang, Tong
TI - The second order projection method in time for the time-dependent natural convection problem
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 299
EP - 315
AB - We consider the second-order projection schemes for the time-dependent natural convection problem. By the projection method, the natural convection problem is decoupled into two linear subproblems, and each subproblem is solved more easily than the original one. The error analysis is accomplished by interpreting the second-order time discretization of a perturbed system which approximates the time-dependent natural convection problem, and the rigorous error analysis of the projection schemes is presented. Our main results of the second order projection schemes for the time-dependent natural convection problem are that the convergence for the velocity and temperature are strongly second order in time while that for the pressure is strongly first order in time.
LA - eng
KW - natural convection problem; projection method; stability; convergence; natural convection problem; projection method; stability; convergence
UR - http://eudml.org/doc/276985
ER -

References

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