Does the element order given in fenics hold when a different element order is specified in gmsh?

1

Hi all,
I’m creating a mixed element space in fenics with

V = VectorElement("Lagrange", mesh.ufl_cell(), 2)
Q = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
MIXED = V * Q

but read in the gmsh tutorial that

Mesh.ElementOrder
Element order (1: first order elements)
Default value: 1
Saved in: General.OptionsFileName

and therefore wonder, does the mixed element specification from fenics still hold when the element order is taken as 1 in gmsh?
Thanks!

2

Yes.

Note that if your geometry contains smooth curves whilst the geometry’s boundary representation is piecewise linear polynomials, you’ll be committing the variational crime (as most of us do every day) that \Omega_h \neq \Omega. Cf. this very old response I wrote on the old forums.

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3

Thanks! I looked at your very old response and I do commit the variational crime. Does it matter for the severeness of this whether the mesh is coarse or fine?

4

Sensitivity to geometry error is problem-dependent. Actually, there are examples of problems for which solutions on a sequence of faceted domains converge to an incorrect solution. The most famous one is the biharmonic problem on faceted approximations of a circle, known as Babuška’s paradox. (You may actually be at some risk of this, since it looks like you’re trying to solve some sort of incompressible flow problem, although it depends on the boundary conditions. Recall that, in 2D, you can reformulate Stokes flow as the biharmonic equation.)

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