Dear Bempp team,

I think there is an implementation error in the barycentric refinement of the **order 1 P space** in **Bempp-cl 0.3.1**. Calling `bempp.api.space.scalar_spaces.p1_barycentric_continuous_function_space(coarse_space)`

returns a *SpaceBuilder* object, where the (numba) surface gradient is set to `_numba_p0_surface_gradient`

(i.e., the surface gradient is the zero vector everywhere) and the order is set to 0. Since the function’s description also mentions “a space of piecewise constant functions”, I suppose that the definition of the barycentric **order 0 P space** and **order 1 P space** have been mixed up. First, I tried to fix this problem locally, however, there still seems to be an issue using the `surface_gradient`

function of the **order 1 P space**’s barycentric refinement (test scripts build upon this function do not give the correct results). Could there be more errors than those mentioned above (in the `bempp.api.space.scalar_spaces.p1_barycentric_continuous_function_space`

function)?

Thank you very much in advance.

Kind regards,

Raphael