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On Time-Discretizations for Generalized Newtonian Fluids

by L. Diening and A. Prohl and M. Ruzicka

(Report number 2002-03)

Abstract
This work improves and extends results of [35] on time-discretization ansatzes for power-law models (p <= 2). New analytical results and techniques from [9] lead to improved convergence rates for a broader range of admissible p's. Then, optimally converging stabilization strategies for the time-discretization are discussed and it is shown how the range of p's enlarges, for which strong solutions of the stabilized system exist.

Keywords: Non-Newtonian fluid flow, degenerate parabolic system, time-discretization, weak and strong solution, shear-dependent viscosity, error analysis, stabilization

@Techreport{DPR02_289,
  author = {L. Diening and A. Prohl and M. Ruzicka},
  title = {On Time-Discretizations for Generalized Newtonian Fluids},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-03.pdf },
  year = {2002}
}

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