Primal–dual formulation for parameter estimation in elastic contact problem with friction

Figures & data

Figure 1. The initial configuration.

Figure 2. The observed state and its von Mises distribution.

Figure 3. The estimated state and its von Mises distribution.

Table 1. The errors between the observations and the estimations.

Errors
Mesh size	$\Vert u-z{\Vert }_H^2$	$\Vert u-z{\Vert }_{H_1}^2$	$|\mu -{\mu }_o|$
1/16	1.5016 e–06	3.5947 e–04	1.985 e–04
1/32	1.4600 e–06	3.4619 e–04	8.8177 e–04
1/64	3.5633 e–06	5.3526 e–05	9.7826 e–02

Table 2. The errors between the observations with noise and the estimations.

Errors with mesh size 1/16
Noise	$\Vert u-z{\Vert }_H^2$	$\Vert u-z{\Vert }_{H_1}^2$	$|\mu -{\mu }_o|$
0.001%	5.9516 e–05	1.3383 e–03	3.8153 e–02
0.01%	4.3047 e–04	6.2533 e–02	1.3384 e–02
0.1 %	1.2913 e–02	4.1043 e+00	2.2265 e–02

Data availability

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.