Further changes

examples/step-87/doc/intro.dox

@@ -94,7 +94,8 @@ set up point-to-point communication patterns.
 
 <h3>Implementation: Utilities::MPI::RemotePointEvaluation</h3>
 
-The algorithm described above is implemented in Utilities::MPI::RemotePointEvaluation and related classes/functions. In this section,
+The algorithm described above is implemented in Utilities::MPI::RemotePointEvaluation
+(short: ``rpe'') and related classes/functions. In this section,
 basic functionalities are briefly summarized. Their advanced
 capabilities will be shown subsequently based on concrete application cases.
 
@@ -153,12 +154,13 @@ Additionally it handles the special case, if points belong to multiple cells
 by taking, e.g., the average, the minimum, or
 the maximum via an optional argument of type EvaluationFlags::EvaluationFlags.
 This occurs when a point lies on a cell boundary or within a small tolerance
-around it.
+around it and might be relevant for discontinuous solution quantities, such
+as in the case of discontinuous Galerkin methods.
 
 
 <h3>Motivation: two-phase flow</h3>
 
-The exemplary mini codes presented in this tutorial
+The minimal code examples (short "mini examples") presented in this tutorial
 are motivated by the application of two-phase-flow simulations formulated in
 a one-fluid setting using a Eulerian framework. In diffuse interface methods,
 the two phases may be implicitly described by a level-set function, here
@@ -256,8 +258,8 @@ are derived from the level-set function.
 
 <h3>Overview</h3>
 
-In the following, we present three simple use cases of Utilities::MPI::RemotePointEvaluation
-(mini examples). We start with discussing a serial code in mini example 0.
+In the following, we present three simple use cases of Utilities::MPI::RemotePointEvaluation.
+We start with discussing a serial code in mini example 0.
 In the subsequent mini examples, advanced problems are solved on distributed meshes:
 <ul>
 <li>mini example 1: we evaluate values and user quantities along a line;</li>

examples/step-87/doc/results.dox

@@ -247,9 +247,8 @@ to derive fast implementations, e.g., for tensor-product elements
 \sum_i \hat{N}^{\text{1D}}_i(\hat{x}_0)
 \hat{u}_{ijk}.
 @f]
-Since only 1D shape functions need to be tabulated, this formulation is faster than
-the original one but still slower than exploiting the tensor-product structure of
-evaluation points as in FEEvaluation.
+Since only 1D shape functions are queried and are re-used in re-occurring terms,
+this formulation is faster than without exploitation of the structure.
 - Utilities::MPI::RemotePointEvaluation is used in multiple places in deal.II. The
 class DataOutResample allows to output results on a different mesh than
 the computational mesh. This is useful if one wants to output the results