Computation of stress point-values (Hencky model)

Next, we consider the computation of the stress value  $\sigma_{11}^{}$(a)  at point  a  (see Figure 3). The results confirm the observations made for the other two tests. The weighted error estimator is not only rather accurate, it can also generate more economical meshes than the other global error estimators.

Tabelle: Results for stress point-value  $\sigma_{11}^{}$(a)  with adaptivity based on the weighted error estimator

N	$\sigma_{11}^{}$	Erelweight	Ratioweight
1,000	9.0275e+01	1.2282e-01	2.1885e+00
2,000	8.7035e+01	8.2528e-02	2.2746e+00
4,000	8.4872e+01	5.5620e-02	1.8710e+00
8,000	8.3323e+01	3.6361e-02	1.9198e+00
16,000	8.2232e+01	2.2790e-02	1.7233e+00
32,000	8.1504e+01	1.3734e-02	1.6212e+00
64,000	8.1014e+01	7.6359e-03	1.5534e+00
128,000	8.0727e+01	4.0618e-03	1.6182e+00
$\infty$	8.0400e+01

Tabelle: Comparison of results for stress point-value  $\sigma_{11}^{}$(a)  for the different error estimators

N	Erelweight	ErelE	ErelZZ
1,000	1.2282e-01	1.2205e-01	1.2320e-01
2,000	8.2528e-02	1.0407e-01	8.7926e-02
4,000	5.5620e-02	5.5785e-02	5.5468e-02
6,000	3.6671e-02	3.6866e-02	3.7033e-02
8,000	2.3709e-02	2.5428e-02	2.4875e-02
10,000	1.5182e-02	1.6799e-02	1.7637e-02
12,000	9.8034e-03	1.0441e-02	1.3457e-02
14,000	6.6807e-03	7.0812e-03	8.5667e-03
16,000	4.0872e-03
18,000	2.7041e-03	4.7628e-03	4.7588e-03

Abbildung: Relative error for stress point-value  $\sigma_{11}^{}$(a)  based on the different error estimators.

Abbildung: Stucture of grids for stress point-value  $\sigma_{11}^{}$(a)  with  N $\approx$ 8, 200