Very minor edits

Author: pefarrell

demos/adaptive_multigrid/adaptive_multigrid.py.rst

@@ -100,7 +100,7 @@ For more information about patch relaxation, see `Using patch relaxation for mul
 Adaptive Mesh Refinement
 -------------------------
 In this section we will discuss how to adaptively refine select elements and add the newly refined mesh into the *AdaptiveMeshHierarchy*.
-For this problem, we will be using the Babuška-Rheinbolt a-posteriori estimate for an element:
+For this problem, we will be using the Babuška-Rheinbolt a posteriori estimate for an element:
 
 .. math::
    \eta_K^2 = h_K^2 \int_K | f + \nabla^2 u_h |^2 \mathrm{d}x + \frac{h_K}{2} \int_{\partial K \setminus \partial \Omega} \llbracket \nabla u_h \cdot n \rrbracket^2 \mathrm{d}s,
@@ -110,7 +110,7 @@ where :math:`K` is the element, :math:`h_K` is the diameter of the element, :mat
 .. math::
    \int_\Omega \eta_K^2 w \mathrm{d}x = \int_\Omega \sum_K h_K^2 \int_K (f + \text{div} (\text{grad} u_h) )^2 \mathrm{d}x w \mathrm{d}x + \int_\Omega \sum_K \frac{h_K}{2} \int_{\partial K \setminus \partial \Omega} \llbracket \nabla u_h \cdot n \rrbracket^2 \mathrm{d}s w \mathrm{d}x
 
-Our approach will be to compute the estimator over all elements and selectively choose to refine only those that contribute most to the error. To compute the error estimator, we use the function below to solve the variational formulation of the error estimator. Since our estimator is a constant per element, we use a DG0 function space.  ::
+Our approach will be to compute the estimator over all elements and selectively choose to refine only those that contribute most to the error. To conveniently compute the error estimator, we use the function below to solve a variational formulation for the error estimator. Since our estimator is a constant per element, we use a DG0 function space.  ::
 
    def estimate_error(mesh, uh):
        W = FunctionSpace(mesh, "DG", 0)
@@ -136,7 +136,7 @@ Our approach will be to compute the estimator over all elements and selectively
            error_est = sqrt(eta_.dot(eta_))
        return (eta, error_est)
 
-The next step is to choose which elements to refine. For this we use Dörfler marking [Dörfler1996]:  
+The next step is to choose which elements to refine. For this we use a simplified variant of Dörfler marking [Dörfler1996]:
 
 .. math::
    \eta_K \geq \theta \text{max}_L \eta_L