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A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation

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  • Yunzhang Zhang
  • Yanren Hou
  • Ganshan Yang

Abstract

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.

Suggested Citation

  • Yunzhang Zhang & Yanren Hou & Ganshan Yang, 2011. "A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-25, July.
    • Handle: RePEc:hin:jnddns:689804
    DOI: 10.1155/2011/689804
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    Cited by:

    1. Nasrin Jahan Nasu & Md. Abdullah Al Mahbub & Shahid Hussain & Haibiao Zheng, 2018. "Two-Level Finite Element Approximation for Oseen Viscoelastic Fluid Flow," Mathematics, MDPI, vol. 6(5), pages 1-20, May.

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