Space-time finite element methods stabilized using bubble function spaces

Figures & data

Figure 1. (a) The space-time domain Q with the boundary parts and its mesh $T_h\left(Q\right)$. (b) The bubble function on the reference triangular mesh element. (c) The bubble function on the reference rectangular mesh element.

Figure 2. Example 1: The solution u on Q.

Table 1. Example 1: The convergence rates r.

$h_s$	$p=1,\kappa =1$	$p=1,\kappa =0.005$
$h_0/2^s$	Convergence rates r
s=1	0.98	1.61
s=2	0.99	1.51
s=3	0.99	1.20
s=4	0.98	1.35
s=5	1.00	1.17
s=6	0.99	1.05
s=7	1.00	1.01

Figure 3. Example 2: The solution u on Q.

Figure 4. Example 3: The solution u on $Q\subset {\mathbb{R}}^3$.

Table 2. Example 2: The convergence rates r.

$h_s$	$p=2,\kappa =1$	$p=2,\kappa =0.005$
$h_0/2^s$	Convergence rates r
s=1	1.73	1.83
s=2	1.98	2.17
s=3	2.01	2.04
s=4	2.00	2.05
s=5	2.00	2.00
s=6	2.00	2.00
s=7	2.00	2.00

Table 3. Example 3: The convergence rates r.

$h_s$	$p=1,\kappa =1$	$p=1,\kappa =0.005$
$h_0/2^s$	Convergence rates r
s=1	1.09	0.60
s=2	0.90	1.06
s=3	0.92	1.16
s=4	0.97	1.15
s=5	1.05	1.10