Apply suggestions from code review

Co-authored-by: Pablo Brubeck <[email protected]>

Author: rckirby

demos/patch/hcurl_riesz_star.py.rst

@@ -67,7 +67,7 @@ patches yield a robust method.::
 Hiptmair proposed a finer space decomposition for Nedelec elements using edge
 patches on the original Nedelec space and vertex patches on the gradient of a Lagrange space. The python type
 preconditioner :class:`~.HiptmairPC` automatically sets up an additive two-level method
-using the auxiliary Lagrange space in a multigrid hierarchy. Therefore, the overall multigrid relaxation composes the edge patches with the auxiliary space relaxation. For the latter, the residual on each level is restricted from H(curl)* into H1* via the adjoint of the gradient, where a vertex patch relaxation is applied to obtain a correction that is prolongoned from H1 into H(curl) via the gradient. ::
+using the auxiliary Lagrange space in a multigrid hierarchy. Therefore, the overall multigrid relaxation composes the edge patches with the auxiliary space relaxation. For the latter, the residual on each level is restricted from the dual of H(curl) into the dual of H1 via the adjoint of the gradient, where a vertex patch relaxation is applied to obtain a correction that is prolonged from H1 into H(curl) via the gradient. ::
 
 
   def hiptmair_params():

demos/patch/stokes_vanka_patches.py.rst

@@ -62,7 +62,7 @@ on the coarsest level of the multigrid hierarchy.::
   }
 
 When we use a matrix-free method, there will not be an assembled matrix to factor
-This forces the matrix to be assembled.::
+on the coarse level. This forces the matrix to be assembled.::
 
   assembled_ldlt = {
       "ksp_type": "preonly",
@@ -115,7 +115,7 @@ matrix to be assembled.  These are quite similar to the options used in
            "pc_patch_precompute_element_tensors": None}},
       mat_type="matfree")
 
-ASMStarPC, on the other hand, does no re-discretization, but extracts the
+:class:`~.ASMStarPC`, on the other hand, does no re-discretization, but extracts the
 patch operators for each patch from the already-assembled global stiffness matrix.::
 
   asm_relax = mg_params(