I would like to create a vector valued finite element space. I know you can do VectorH1, but what if the number of components is not equal to the spatial dimension?
For example, suppose I want an H1 vector-valued function (defined on a 3-D mesh), with 5 components. How should I do it? I guess I could do this:
V = H1(mesh,order=k, dirichlet=“whatever”)
X = FESpace([V,V,V,V,V])
Would that work?
Also, is there a tensor-valued finite element space option? Say for symmetric matrices? That are trace-free?
That one shall work, but you need to then build your own differential operators.
The “MatrixValued” option can do tensors, which includes full tensor, symmetric, or deviatoric tensor. I guess the symmetric deviatoric tensor might be the one you are looking for.
Sigma = MatrixValued(H1(mesh, order=2), mesh.dim, symmetric=True, deviatoric=True)
Thanks for this. But there isn’t a way to set the number of components in VectorH1? That should be an option.
You can set the dimensions explicitly by
fes = H1(mesh, order=k, dim=5)
or using a product space with the syntax
fes = H1(mesh, order=k)**5