Stability and convergence of the higher projection method for the time-dependent viscoelastic flow problem

Stability and convergence of the higher projection method for the time-dependent viscoelastic... In this paper, the time discrete higher order projection method is proposed and analyzed for the time-dependent viscoelastic flow problem. Our numerical method is based on the time iterative discrete schemes. By the projection method, the considered problem is decoupled into two linear subproblems: One is for the velocity and the other is for the pressure. Unconditional stability of the numerical schemes is established. Convergence results for the velocity and pressure are also derived. Our main results of this paper are that the convergence analysis for the velocity is weakly second order and for the pressure is weakly first order. Finally, some numerical examples are provided to confirm the performances of the developed numerical algorithms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational and Applied Mathematics Elsevier

Stability and convergence of the higher projection method for the time-dependent viscoelastic flow problem

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier B.V.
ISSN
0377-0427
eISSN
1879-1778
D.O.I.
10.1016/j.cam.2017.12.045
Publisher site
See Article on Publisher Site

Abstract

In this paper, the time discrete higher order projection method is proposed and analyzed for the time-dependent viscoelastic flow problem. Our numerical method is based on the time iterative discrete schemes. By the projection method, the considered problem is decoupled into two linear subproblems: One is for the velocity and the other is for the pressure. Unconditional stability of the numerical schemes is established. Convergence results for the velocity and pressure are also derived. Our main results of this paper are that the convergence analysis for the velocity is weakly second order and for the pressure is weakly first order. Finally, some numerical examples are provided to confirm the performances of the developed numerical algorithms.

Journal

Journal of Computational and Applied MathematicsElsevier

Published: Aug 15, 2018

References

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