A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation
A defect-correction mixed finite element method for solving the time-dependent Johnson-Segalman viscoelastic equations in two dimensions is given. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the resulting residual i...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/689804 |
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| Summary: | A defect-correction mixed finite element method for solving the time-dependent
Johnson-Segalman viscoelastic equations in two dimensions is given. In
the defect step, the constitutive equation is computed with the artificially
reduced Weissenberg parameter for stability, and the resulting residual is
corrected in the correction step on the same grid. A streamline upwind
Petrov-Galerkin (SUPG) approximation is used to stabilize the hyperbolic
character of the constitutive equation for the stress. We establish a priori
error estimates for the defect step and the first correction step of the defect
correction method. The derived theoretical results are supported by
numerical tests. |
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| ISSN: | 1026-0226 1607-887X |