Add 'Auto-refinement' section at the end of README.md and reference it

in CHANGELOG and the beginning of README.md.

CHANGELOG

@@ -16,7 +16,8 @@ Version 4.2.1 (development)
   data (mesh and grid function). The new refinement is chosen to be sufficient
   for resolving the curvature of the data, but only if we can do that with less
   than 2M vertices and 16 refinements. Otherwise, we print a warning and the
-  user may still needs to press 'o' to fully resolve the data.
+  user may still need to press 'o' to fully resolve the data. For more details,
+  see the section Auto-refinement in README.md.
 
 - Significantly improved memory usage.
 

README.md

@@ -68,6 +68,12 @@ is a partial list of the available functionality. Some of these keys can also be
 provided as input, using the `-k` command-line option and the `keys` script
 command.
 
+For high-order meshes and/or solution data, GLVis performs element subdivision
+to try to represent the data more accurately. However, for highly-varying data
+or large meshes, the auto-selected subdivision factor (see the
+[Auto-refinement](#auto-refinement) section below) may not be sufficient -- use
+the keys <kbd>o</kbd> / <kbd>O</kbd>, described below, to manually adjust the
+subdivision factor.
 
 SPDX-License-Identifier: BSD-3-Clause <br>
 LLNL Release Number: LLNL-CODE-443271 <br>
@@ -298,3 +304,46 @@ Key commands
   - `x`-component: `v_x`
   - `y`-component: `v_y`
   - `z`-component: `v_z`
+
+## Auto-refinement
+
+The GLVis auto-refinement algorithm selects a subdivision factor trying to
+achieve an accurate representation of high-order meshes and solution data while
+keeping the initial time to visualize the data reasonable. The algorithm can be
+summarized as follows:
+- GLVis draws surface elements; the number of drawn elements, `ne`, is either:
+  - the number of elements in the mesh for 2D meshes (including surface meshes,
+    i.e. 2D meshes embedded in 3D space), or
+  - the number of boundary mesh elements described by the mesh in 3D.
+- A tentative upper limit on the number of vertices to be drawn is defined based
+  on the maximum order of the mesh and the solution, `max_order`:
+  ```
+  max_vert = ne * (max_order + 1) * (max_order + 1)
+  ```
+- To allow more accurate representation for small meshes, this number is
+  potentially increased:
+  ```
+  max_vert = max(max_vert, 100 000)
+  ```
+- To keep the time to initially visualize the data reasonable, this number is
+  potentially reduced:
+  ```
+  max_vert = min(max_vert, 2 000 000)
+  ```
+- Finally, the subdivision factor `ref` is chosen to be the largest number such
+  that:
+  - the number of vertices needed to draw the `ne` surface elements with `ref`
+    subdivisions does not exceed `max_vert`:
+    ```
+    ne * (ref + 1) * (ref + 1) <= max_vert
+    ```
+  - for large meshes where the above limit cannot be satisfied, set `ref = 1`
+  - for small meshes, avoid excessive refinements:
+    ```
+    ref <= 16
+    ```
+
+Note that, for highly-varying data or large meshes, this auto-selected
+subdivision factor may not be sufficient for accurate representation. In such
+cases the sudivision can be manually adjusted using the keys <kbd>o</kbd> /
+<kbd>O</kbd>, described above.