How does FEniCS integrate an expression?

Question

I have a user-defined expression "fun" that is everywhere either 0.0 or -1.0. However, if I run

print assemble(conditional(lt(fun, const), 1.0, 0.0)*dx, mesh=mesh)

where const is -0.1, -0.2, -0.3, ..., then, although I would expect to obtain identical results, the results look like
"34.193..., 34.193..., 25.8265..., 25.8265..., 19.424...", i.e. it jumps whenever const reaches some threshold. Why is it? I thought that FEniCS uses some kind of Gaussian quadratures for integrating and fun is <-0.1 iff it is <-0.5.

Answer 1

The FEniCS libraries interpolate functions in a finite element space. To be sure of which space it being using, you can supply a FiniteElement argument to an Expression.

If you want to have something evaluated at quadrature points, use a 'quadrature element'.

Comments

Ok, thanks. So is it so that FEniCS chooses somehow some FunctionSpace on the mesh and computes something like the projection of the expression to this space first?

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It doesn't project. It interpolates.