Approximation of the p-stokes equations with equal-order finite elements
Non-Newtonian fluid motions are often modeled by the p-Stokes equations with power-law exponent p∈(1,∞)p∈(1,∞){p\in(1,\infty)} . In the present paper we study the discretization of the p-Stokes equations with equal-order finite elements. We propose a stabilization scheme for the pressure-gradient ba...
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2013
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| In: |
Journal of mathematical fluid mechanics
Year: 2012, Volume: 15, Issue: 1, Pages: 65-88 |
| ISSN: | 1422-6952 |
| DOI: | 10.1007/s00021-012-0095-0 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s00021-012-0095-0 Verlag, Volltext: https://link.springer.com/content/pdf/10.1007%2Fs00021-012-0095-0.pdf Verlag, Volltext: https://link.springer.com/article/10.1007/s00021-012-0095-0 
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| Author Notes: | Adrian Hirn |
MARC
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| 520 | |a Non-Newtonian fluid motions are often modeled by the p-Stokes equations with power-law exponent p∈(1,∞)p∈(1,∞){p\in(1,\infty)} . In the present paper we study the discretization of the p-Stokes equations with equal-order finite elements. We propose a stabilization scheme for the pressure-gradient based on local projections. For p∈(1,∞)p∈(1,∞){p\in(1,\infty)} the well-posedness of the discrete problems is shown and a priori error estimates are proven. For p∈(1,2]p∈(1,2]{p\in(1,2]} the derived a priori error estimates provide optimal rates of convergence with respect to the supposed regularity of the solution. The achieved results are illustrated by numerical experiments. | ||
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