Hello again, 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? Thank you again for your time. Hoping I can get up to speed to contribute back in the future. Best regards, Doug -- 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.
