On the Accuracy of Finite Element and Finite Difference Predictions of Non-Newtonian Slot Pressures for a Maxwell Fluid

  • David S. Malkus
  • Michael F. Webster
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 12)


Plane slow flow of a Maxwell fluid over a transverse slot is considered. Results are computed by a finite difference method (FDM) using the differential form of the constitutive equation, and by a finite element method (FEM) using the integral form. Even on fine grids, the two methods produce different results, particularly at low D e . However, extrapolation of the results to zero mesh spacing shows excellent agreement between the two methods. Hence both methods are convergent with mesh refinement, but high accuracy would require extremely fine meshes. An explanation is provided for why it is unreasonable to expect either method accurately to obtain the singular limit of P e /N 1 as D e → 0. Also an explanation for the errors at very low D e is offered. If we presume the the second-order fluid (SOE) result holds for very low D e (i. e. P e = N 1/4), both the FEM and FDM predict only minor deviation from this value for the Maxwell fluid, in the range 0 ≤ D e ≤ 1.


Error Model Mesh Refinement Finite Difference Method Discretization Error Error Indicator 
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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • David S. Malkus
    • 1
    • 2
  • Michael F. Webster
    • 3
  1. 1.Mathematics Research CenterMadisonUSA
  2. 2.Department of Engineering MechanicsUniversity of Wisconsin - MadisonMadisonUSA
  3. 3.Department of Mathematics and Computer ScienceUniversity College of SwanseaSwanseaUK

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