[Web] Add the result comparison figure of Theis' test (#2080)

* [Web] Added a figure about the result comparison of Theis' test

* [web] Added a table of data to Theis' example

web/content/docs/benchmarks/liquid-flow/liquid-flow-theis-problem.md

@@ -55,3 +55,184 @@ $$
 where $\gamma\approx$ 0.5772 is the Euler-Mascheroni constant. For practical purposes, the simplest approximation of $W(u)$ was proposed as $W(u)=-0.5772-lnu$  for $u <$ 0.05. Other more exact approximations of the well function were summarized by R. Srivastava and A. Guzman-Guzman
 
 ## Results and evaluation
+
+The following figure compares the analytical solution, the result by ogs5, and
+ the result by ogs6 (labeled as `pressure`) within the range that satisfies
+ $u <$ 0.05.
+{{< img src="../theis_comparison.png" >}}
+The figure shows that there is a good match between the analytical solution and
+ the numerical solution obtained by using ogs5 or ogs6.
+
+<p>Some of the data of the above curves are given in the following table.</p>
+<table>
+<caption>Comparison of solutions (where <em>Distance</em> means the distance
+ from the position where the source term is applied).</caption>
+<tbody>
+<tr class="odd">
+<td style="text-align: left;">Distance</td>
+<td style="text-align: left;">Analytic</td>
+<td style="text-align: left;">OGS5</td>
+<td style="text-align: left;">OGS6</td>
+<td style="text-align: left;">Error</td>
+<td style="text-align: left;">Error</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;"></td>
+<td style="text-align: left;">Solution (<span class="math inline"><em>h</em><sub><em>a</em></sub></span>)</td>
+<td style="text-align: left;">(<span class="math inline"><em>h</em><sub>5</sub></span>)</td>
+<td style="text-align: left;">(<span class="math inline"><em>h</em><sub>6</sub></span>)</td>
+<td style="text-align: left;">(<span class="math inline">$$|\frac{h_5-h_a}{h_a}|$$</span>)</td>
+<td style="text-align: left;">(<span class="math inline">$$|\frac{h_6-h_a}{h_a}|$$</span>)</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">0</td>
+<td style="text-align: left;">12.8141</td>
+<td style="text-align: left;">12.474</td>
+<td style="text-align: left;">12.474</td>
+<td style="text-align: left;">0.0265</td>
+<td style="text-align: left;">0.0272</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">1.21799</td>
+<td style="text-align: left;">8.9441</td>
+<td style="text-align: left;">8.79341</td>
+<td style="text-align: left;">8.79341</td>
+<td style="text-align: left;">0.0168</td>
+<td style="text-align: left;">0.0171</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">2.43597</td>
+<td style="text-align: left;">7.48878</td>
+<td style="text-align: left;">7.34717</td>
+<td style="text-align: left;">7.34717</td>
+<td style="text-align: left;">0.0189</td>
+<td style="text-align: left;">0.0192</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">3.65396</td>
+<td style="text-align: left;">6.59978</td>
+<td style="text-align: left;">6.46176</td>
+<td style="text-align: left;">6.46176</td>
+<td style="text-align: left;">0.0209</td>
+<td style="text-align: left;">0.0213</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">4.87195</td>
+<td style="text-align: left;">5.94548</td>
+<td style="text-align: left;">5.81072</td>
+<td style="text-align: left;">5.81072</td>
+<td style="text-align: left;">0.0226</td>
+<td style="text-align: left;">0.0231</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">6.08994</td>
+<td style="text-align: left;">5.43381</td>
+<td style="text-align: left;">5.30267</td>
+<td style="text-align: left;">5.30267</td>
+<td style="text-align: left;">0.0241</td>
+<td style="text-align: left;">0.0247</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">7.30792</td>
+<td style="text-align: left;">5.00981</td>
+<td style="text-align: left;">4.88283</td>
+<td style="text-align: left;">4.88283</td>
+<td style="text-align: left;">0.0253</td>
+<td style="text-align: left;">0.0260</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">8.52591</td>
+<td style="text-align: left;">4.65012</td>
+<td style="text-align: left;">4.52793</td>
+<td style="text-align: left;">4.52793</td>
+<td style="text-align: left;">0.0262</td>
+<td style="text-align: left;">0.0269</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">8.83041</td>
+<td style="text-align: left;">4.56714</td>
+<td style="text-align: left;">4.44623</td>
+<td style="text-align: left;">4.44623</td>
+<td style="text-align: left;">0.0264</td>
+<td style="text-align: left;">0.0271</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">9.4394</td>
+<td style="text-align: left;">4.4116</td>
+<td style="text-align: left;">4.29344</td>
+<td style="text-align: left;">4.29344</td>
+<td style="text-align: left;">0.0267</td>
+<td style="text-align: left;">0.0275</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">10.6574</td>
+<td style="text-align: left;">4.12707</td>
+<td style="text-align: left;">4.01501</td>
+<td style="text-align: left;">4.01501</td>
+<td style="text-align: left;">0.0271</td>
+<td style="text-align: left;">0.0279</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">15.2248</td>
+<td style="text-align: left;">3.28072</td>
+<td style="text-align: left;">3.19698</td>
+<td style="text-align: left;">3.19698</td>
+<td style="text-align: left;">0.0255</td>
+<td style="text-align: left;">0.0261</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">20.0968</td>
+<td style="text-align: left;">2.61899</td>
+<td style="text-align: left;">2.57517</td>
+<td style="text-align: left;">2.57517</td>
+<td style="text-align: left;">0.0167</td>
+<td style="text-align: left;">0.0170</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">22.8373</td>
+<td style="text-align: left;">2.31338</td>
+<td style="text-align: left;">2.29626</td>
+<td style="text-align: left;">2.29626</td>
+<td style="text-align: left;">0.0074</td>
+<td style="text-align: left;">0.0074</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">24.0553</td>
+<td style="text-align: left;">2.18892</td>
+<td style="text-align: left;">2.1846</td>
+<td style="text-align: left;">2.1846</td>
+<td style="text-align: left;">0.0019</td>
+<td style="text-align: left;">0.0019</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">25.2732</td>
+<td style="text-align: left;">2.07055</td>
+<td style="text-align: left;">2.07958</td>
+<td style="text-align: left;">2.07958</td>
+<td style="text-align: left;">0.0043</td>
+<td style="text-align: left;">0.0043</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">25.5777</td>
+<td style="text-align: left;">2.04164</td>
+<td style="text-align: left;">2.05407</td>
+<td style="text-align: left;">2.05407</td>
+<td style="text-align: left;">0.0060</td>
+<td style="text-align: left;">0.0060</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">29.8407</td>
+<td style="text-align: left;">1.67134</td>
+<td style="text-align: left;">1.73518</td>
+<td style="text-align: left;">1.73518</td>
+<td style="text-align: left;">0.0381</td>
+<td style="text-align: left;">0.0367</td>
+</tr>
+</tbody>
+</table>
+<p>The analytical solutions are for an ideal problem with point wise pumping
+ term. While for the FEM analysis, the point wise source value is distributed to
+ the surface of a small hole around the source point in order to avoid the
+ singularity. One can see from the table that the precisions of the FEM
+ solutions are still acceptable with such transform of the point pumping
+ term.</p>