Dear Jimmy,
  Thank you! Your answer solved my question. I had the wrong impression
that higher-order polynomials will give more base functions. Shape
functions just play the role of interpolation and construct the solution
space. It could be a high-order polynomial but only one base function per
node.  Thank you very much!
Best regards

On Sun, Aug 2, 2020 at 11:50 PM Jimmy Ho <jimmyho0...@gmail.com> wrote:

> Hi Yuesu,
>
> To be more precise: Yes, you do have two sets of basis functions in each
> element. A quadratic one for interpolating the vector components, and a
> linear one for interpolating the scalar. But when calculating DOFs
> associated with the vector components, you should only count the basis
> functions that interpolate those components, which is one basis function
> per node.
>
> Hope this helps!
>
> Best,
> Jimmy
>
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-- 
Yuesu Jin,
Ph.D student,
University of Houston,
College of Natural Sciences and Mathematics,
Department of Earth and Atmospheric Sciences,
Houston, Texas 77204-5008
346-404-2062

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