From: Marc Fehling Date: Tue, 23 May 2023 20:39:16 +0000 (-0600) Subject: parallel in time: Convert tabular to markdown. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F145%2Fhead;p=code-gallery.git parallel in time: Convert tabular to markdown. --- diff --git a/parallel_in_time/Readme.md b/parallel_in_time/Readme.md index ff165c4..a7e4cb2 100644 --- a/parallel_in_time/Readme.md +++ b/parallel_in_time/Readme.md @@ -113,29 +113,21 @@ where $\Delta \epsilon_n$ is the convergence rate of error $\epsilon$ between a Shown in Table 1 are the errors of the $\textrm{L}^2$, $\textrm{H}^1$, and $\textrm{L}^\infty$ norms as the mesh is refined, and shown in Table 2 is the convergence rate. The $\Delta t$ is reduced by a factor of 2 for every global refinement of the mesh. -@f{align} - \begin{tabular}{|c|c|c|c|c|c|} \hline - cycles & \# cells & \# dofs & $\textrm{L}^2$-error & $\textrm{H}^1$-error & $\textrm{L}^\infty$-error \\ \hline - 125 & 48 & 65 & 6.036e-03 & 6.970e-02 & 7.557e-03\\ \hline - 250 & 192 & 225 & 1.735e-03 & 3.414e-02 & 2.721e-03 \\ \hline - 500 & 768 & 833 & 4.513e-04 & 1.690e-02 & 7.410e-04 \\ \hline - 1000 & 3072 & 3201 & 1.140e-04 & 8.426e-03 & 1.877e-04 \\ \hline - 2000 & 12288 & 12545 & 2.859e-05 & 4.209e-03 & 4.715e-05 \\ \hline - \end{tabular} -@f} - -@f{align} - \begin{tabular}{|c|c|c|c|c|c|} \hline - cycles & \# cells & \# dofs & Slope $\textrm{L}^2$ & Slope $\textrm{H}^1$ & Slope $\textrm{L}^\infty$ \\ \hline - 125 & 48 & 65 & --- & --- & --- \\ \hline - 250 & 192 & 225 & 1.798 & 1.030 & 1.474 \\ \hline - 500 & 768 & 833 & 1.943 & 1.014 & 1.877 \\ \hline - 1000 & 3072 & 3201 & 1.985 & 1.004 & 1.981 \\ \hline - 2000 & 12288 & 12545 & 1.995 & 1.001 & 1.993 \\ \hline - \end{tabular} -@f} - - +| cycles | # cells | # dofs | $\textrm{L}^2$-error | $\textrm{H}^1$-error | $\textrm{L}^\infty$-error | +| :----: | :-----: | :----: | :------------------: | :------------------: | :-----------------------: | +| 125 | 48 | 65 | 6.036e-03 | 6.970e-02 | 7.557e-03 | +| 250 | 192 | 225 | 1.735e-03 | 3.414e-02 | 2.721e-03 | +| 500 | 768 | 833 | 4.513e-04 | 1.690e-02 | 7.410e-04 | +| 1000 | 3072 | 3201 | 1.140e-04 | 8.426e-03 | 1.877e-04 | +| 2000 | 12288 | 12545 | 2.859e-05 | 4.209e-03 | 4.715e-05 | + +| cycles | # cells | # dofs | Slope $\textrm{L}^2$ | Slope $\textrm{H}^1$ | Slope $\textrm{L}^\infty$ | +| :----: | :-----: | :----: | :------------------: | :------------------: | :-----------------------: | +| 125 | 48 | 65 | --- | --- | --- | +| 250 | 192 | 225 | 1.798 | 1.030 | 1.474 | +| 500 | 768 | 833 | 1.943 | 1.014 | 1.877 | +| 1000 | 3072 | 3201 | 1.985 | 1.004 | 1.981 | +| 2000 | 12288 | 12545 | 1.995 | 1.001 | 1.993 | The convergence rate is plotted as a function of the grid spacing in the figure below. As can be seen, the slope converges at a second order rate for the $\textrm{L}^2$ and $\textrm{L}^\infty$ norms and at a first order rate for the $\textrm{H}^1$ norms.