Abstract

Certain rheological behaviors of fluids in engineering sciences are modeled by power law ansatz with $p\in(1,2]$. In the present paper a semi-implicit time discretization scheme for such fluids is proposed. The main result is the optimal $\mathcal{O}(k)$ error estimate, where k is the time step size. Our results hold in the range $p\in(3/2,2]$ (in the three-dimensional setting) for strong solutions of the continuous problem, whose existence is guaranteed under appropriate assumptions on the data. The estimates are uniform with respect to the degeneracy parameter $\delta\in[0,\delta_0]$ of the extra stress tensor. Additional regularity properties of the solution of the discrete problem are proved.

MSC codes

  1. 76A05
  2. 35K65
  3. 65M06
  4. 35Q35

Keywords

  1. non-Newtonian fluids
  2. shear dependent viscosity
  3. time discretization
  4. error analysis
  5. degenerate parabolic systems

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Information & Authors

Information

Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 2177 - 2202
ISSN (online): 1095-7170

History

Submitted: 2 April 2008
Accepted: 10 March 2009
Published online: 10 June 2009

MSC codes

  1. 76A05
  2. 35K65
  3. 65M06
  4. 35Q35

Keywords

  1. non-Newtonian fluids
  2. shear dependent viscosity
  3. time discretization
  4. error analysis
  5. degenerate parabolic systems

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