Is it possible to increase the order of the finite element space locally?

Question

Exampe:

Let $\Omega$ be a disc of radius 1 centered in the origin,
and let $D$ be a disc of radius 0.5 centered in the origin as well.

Is it possible to solve
$$-\Delta u = 1 \quad \text{in } \Omega\,, \quad u = 0 \quad\text{on } \partial\Omega\,,$$
using first order continuous Lagrangian finite elements in $\Omega\setminus D$ and
second order continuous Lagrangian finite elements in $D$?

Answer 1

FEniCS does not support this (in a straightforward manner).

Comments

It would be great if this may be possible in general! But now, is there any non-straigthforward way to do this or a suggestion i could try?