8. Summary of results in 2D#
TRIA3 |
QUAD4 |
TRIA6 |
QUAD8 |
QUAD9 |
||
|
Exact |
3.44% |
2.48% |
1.17% |
0.697% |
0.695% |
|
3.28% |
2.28% |
0.95% |
0.22% |
0.21% |
|
|
3.49% |
2.37% |
1.29% |
0.687% |
0.66% |
|
|
|
0.952 |
0.919 |
0.810 |
0.321 |
0.306 |
|
1.013 |
0.958 |
1.099 |
0.985 |
0.951 |
|
Node constraints are, within the set, best approximated with \(\mathrm{ZZ2}\), especially for order 2 items. If we make it tender
towards 0, the convergence rates with \(h\) of
are greater by the \(\mathrm{ZZ2}\) method for all element types than the \(\mathrm{ZZ1}\) method (
is the smoothed stress).
The estimator \(\mathrm{ZZ1}\) is not reliable for elements of order 2, the nodal constraints remain correct. In this particular case, it can be verified that
when
, which shows that continuous global smoothing is insufficient to estimate the error in the case of a solution without a singularity (case of this test).
On the other hand, \(\mathrm{ZZ2}\) is reliable and asymptotically accurate (
when
).