elementwise_integral doesn't respect quadrature rules

[inducer]

As implemented here:

grudge/grudge/reductions.py

Lines 455 to 470 in f3d986b

	if len(args) == 1:
	vec, = args
	dd = dof_desc.DOFDesc("vol", dof_desc.DISCR_TAG_BASE)
	elif len(args) == 2:
	dd, vec = args
	else:
	raise TypeError("invalid number of arguments")
	dd = dof_desc.as_dofdesc(dd)
	from grudge.op import _apply_mass_operator
	ones = dcoll.discr_from_dd(dd).zeros(vec.array_context) + 1.0
	return elementwise_sum(
	dcoll, dd, vec * _apply_mass_operator(dcoll, dd, dd, ones)
	)

It always falls into the mass-matrix logic, which is valid for nodal-interpolatory grids, but not quadrature grids.

cc @thomasgibson

[inducer]

Could implement, per group, as:

res = DOFArray(
    dof_array.array_context,
    tuple([
        actx.np.einsum("ei,i,ei->e",
            dof_array.data[i], quad_weights, area_elements.data[i]
            ).reshape(-1, 1)
        for grp, vec_grp_ary, ae_grp_ary in zip(
            discr.groups, vec.data, area_elements.data
    ])