From 40f08b94b15c14d67d24f4aff8922c432ccb9f9c Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Fri, 3 Sep 2021 13:26:59 -0600 Subject: [PATCH] Add table for k=3 to the results section. --- examples/step-82/doc/results.dox | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/examples/step-82/doc/results.dox b/examples/step-82/doc/results.dox index 2bdee1440a..9fc5b85289 100644 --- a/examples/step-82/doc/results.dox +++ b/examples/step-82/doc/results.dox @@ -113,6 +113,20 @@ $H^1$ norms, but is sub-optimal for the $L_2$ norm. Incidentally, this also matches the results seen in step-47 when using polynomial degree $k=2$. +Indeed, just like in step-47, we can regain the optimal convergence +order if we set the polynomial degree of the finite elements to $k=3$ +or higher. Here are the numbers for $k=3$: + + + + + + + + + +
n_ref n_cells n_dofs error H2 rate error H1 rate error L2 rate
1 4 36 1.451e-02 -- 5.494e-04 -- 3.035e-05 --
2 16 144 3.565e-03 2.02 6.870e-05 3.00 2.091e-06 3.86
3 64 576 8.891e-04 2.00 8.584e-06 3.00 1.352e-07 3.95
4 256 2304 2.223e-04 2.00 1.073e-06 3.00 8.594e-09 3.98
5 1024 9216 5.560e-05 2.00 1.341e-07 3.00 5.418e-10 3.99
6 4096 36864 1.390e-05 2.00 1.676e-08 3.00 3.245e-11 4.06
+

Possible extensions

-- 2.39.5