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An analysis of the Rayleigh–Stokes problem for a generalized second-grade fluid

Bazhlekova, E; Lazarov, R; Jin, B; Zhou, Z; (2015) An analysis of the Rayleigh–Stokes problem for a generalized second-grade fluid. Numerische Mathematik , 131 (1) pp. 1-31. 10.1007/s00211-014-0685-2. Green open access

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Abstract

We study the Rayleigh–Stokes problem for a generalized second-grade fluid which involves a Riemann–Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data (Formula presented.), including (Formula presented.). A space semidiscrete Galerkin scheme using continuous piecewise linear finite elements is developed, and optimal with respect to initial data regularity error estimates for the finite element approximations are derived. Further, two fully discrete schemes based on the backward Euler method and second-order backward difference method and the related convolution quadrature are developed, and optimal error estimates are derived for the fully discrete approximations for both smooth and nonsmooth initial data. Numerical results for one- and two-dimensional examples with smooth and nonsmooth initial data are presented to illustrate the efficiency of the method, and to verify the convergence theory.

Type: Article
Title: An analysis of the Rayleigh–Stokes problem for a generalized second-grade fluid
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00211-014-0685-2
Publisher version: http://dx.doi.org/10.1007/s00211-014-0685-2
Language: English
Additional information: Copyright © The Author(s) 2014. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1461687
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