Doug,
> I am now looking into adding vector-valued equations to my current
> framework. The goal will be to do some hp-adaptive Navier-Stokes flow
> simulation using Discontinuous Galerkin. I have read "Handling vector
> valued problems", went through most of the vector-valued examples, and
> saw lecture 19 and 20 from Prof. Bangerth. The common denominator seems
> to be: use FESystem to combine multiple FiniteElement together.
>
> However, I will not need to use mixed finite elements, and therefore, my
> FiniteElement will always be the same for all components of the solution
> for a given cell. As a result, I would expand my vector solution as a
> linear combination of vector-valued coefficients (degrees of freedom),
> and scalar trial functions. As for the trial function, the vector trial
> function can be taken "component-wise" as explained in step-8.
> Basically, Eq. 7-9 of Bassi and Rebay's paper show how I would only need
> scalar basis functions defined by a single FiniteElement
>
> Bassi, F., and Rebay, S., “High-order accurate discontinuous finite
> element solution of the 2D Euler equations,”/Journal of
> Computational Physics/, vol. 138, 1997, pp. 251–285.
>
>
> Therefore, it doesn't seem like I would need a FESystem. If anything,
> the FESystem makes the code more complex and less readable in my case,
> since each entry of the vector-valued bases would just be copies of each
> other.
>
> Is the use of FESystem somehow simplifying my code in any aspect?
> The two main things I can think of is
>
> * Easy access to the "global solution vector" index through the
> DoFHandler and its re-ordering functions.
> * Performing operator-like operations on similar equations (e.g. 3
> momentum equations)
>
> Am I missing something?
This is it. We've generally found that code is more readable by using
systems of elements and extractors, because you are implicitly
documenting code if you use extractors. This is more difficult to do
when you re-use the same element. But it's possible, of course, and may
even be more efficient.
You probably want to look at step-35 which does something similar to
what you proposal.
Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups
"deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to dealii+unsubscr...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.
