Thank you for your prompt response.
Q1) I am not familiar with RE_RaviartThomas elements, is it a vector type
element having dim components,
that is how I see it used in step-20 to represent components of velocities?
Q2) How does my FE_System for u and \sigma together look like, let's say I
modify step-8 as?
If RT elements have dim components, then the following system wouldn't make
sense.
FE_System(FE_Q<dim>(degree), dim, FE_RaviartThomas<dim>(degree), dim*dim)
or the below
FE_System(FE_Q<dim>(degree), dim, FE_RaviartThomas<dim>(degree), dim)
Q3) Such a system can only be solved using BlockMatrix and BlockVector i.e
not using components alone?
I ask this question because I gather from different postings that
PETSc does not work with Block format.
Q4) How do I group components into tensors? Is there a tutorial where a *tensor
system is solved* you can point me to?
Many thanks,
Karthi.
On Mon, Feb 8, 2021 at 6:30 PM Wolfgang Bangerth <[email protected]>
wrote:
> On 2/8/21 9:10 AM, Karthi wrote:
> >
> > I want to solve a linear elasticity for unknowns displacement (u) and
> stress
> > (\sigma) simultaneously using a mixed formulation. I have_attached_ the
> > revenant strong and weak form of the problem. For u is the discretized
> using
> > Lagrange elements and \sigma using Raviart-Thomas elements.
> >
> > Step-20 has an example using mixed formulation, were RT elements were
> used for
> > velocity which has dim components. Whereas in my case were RT elements
> would
> > have dim x dim components for stress. How do I go about it?
>
> In analogy to step-8, where you create an FESystem that contains several
> scalar finite elements, you will want to create an FESystem that contains
> several FE_RaviartThomas elements.
>
> There is also FEValuesExtractors::Tensor that allows you to group
> components
> into tensors, in the same way as you can do for vectors.
>
> Best
> W.
>
>
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> Wolfgang Bangerth email: [email protected]
> www: http://www.math.colostate.edu/~bangerth/
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