<p>
The main emphasis in this example is the handling of locally refined
-grids. In our approach to adaptivity, we use grids of which
-neighboring cells may be refined a different number of times, and then
-there result nodes on the interfaces of cells which belong to one
-side, but are unbalanced on the other. We call these ``hanging nodes''.
+grids. The approach to adaptivity chosen in deal.II us to use grids in which
+neighboring cells may be refined a different number of times. This then
+results in nodes on the interfaces of cells which belong to one
+side, but are unbalanced on the other. The common term for these is
+“hanging nodes”.
</p>
<p>
To guarantee that the global solution is continuous at these nodes as
well, we have to state some additional constraints on the values of
-the solution at these nodes, and we will show how to obtain these
-constraints and how to use them in the solution of the linear system
-of equations.
+the solution at these nodes. In the program below, we will show how we
+can get these constraints from the library, and how to use them in the
+solution of the linear system of equations.
</p>
<p>
problems. Although it will create non-optimal meshes for other
equations, it is often a good way to quickly produce meshes that are
well adapted to the features of solutions, such as regions of great
-variation or discontinuities. Although the error estimator (and its
+variation or discontinuities. Since it was developed by Kelly and
+co-workers, we often refer to it as the “Kelly refinement
+indicator” in the library, documentation, and mailing list. The
+class that implements it is called
+“KellyErrorEstimator”. Although the error estimator (and
+its
implementation in the deal.II library) is capable of handling variable
coefficients in the equation, we will not use this feature since we
are only interested in a quick and simple way to generate locally
<p>
The only other new thing is a method to catch exceptions in the
-``main'' function in order to output some information in case the
+“main” function in order to output some information in case the
program crashes for some reason.
</p>