Stable finite element methods for the Stokes problem
The mixed finite element scheme of the Stokes problem with pressure stabilization is analyzed for the cross-grid Pk−Pk−1elements, k≥1, using discontinuous pressures. The Pk+−Pk−1 elements are also analyzed. We prove the stability of the scheme using the macroelement technique. The order of convergen...
| Published in: | International Journal of Mathematics and Mathematical Sciences |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200002908 |
| Summary: | The mixed finite element scheme of the Stokes problem with
pressure stabilization is analyzed for the cross-grid Pk−Pk−1elements, k≥1, using discontinuous pressures. The Pk+−Pk−1 elements are also analyzed. We prove the stability of the scheme using the
macroelement technique. The order of convergence follows from the standard
theory of mixed methods. The macroelement technique can also be applicable
to the stability analysis for some higher order methods using continuous
pressures such as Taylor-Hood methods, cross-grid methods, or iso-grid
methods. |
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| ISSN: | 0161-1712 1687-0425 |