Fully discrete DPG methods for the Kirchhoff–Love plate bending model
Thomas Führer and Norbert Heuer
Comput. Methods Appl. Mech. Engrg. 343, 550–571, 2019.
We extend the analysis and discretization of the Kirchhoff–Love plate bending problem from
[T. Führer, N. Heuer, A.H. Niemi, An ultraweak formulation of the Kirchhoff–Love plate bending model
and DPG approximation,
arXiv:1805.07835,
DOI:10.1090/mcom/3381]
in two aspects. First, we present a well-posed formulation and quasi-optimal
DPG discretization that includes the gradient of the deflection.
Second, we construct Fortin operators that prove the well-posedness and quasi-optimal convergence
of lowest-order discrete schemes with approximated test functions for both formulations.
Our results apply to the case of non-convex polygonal plates where shear forces can be
less than L²-regular. Numerical results illustrate expected convergence orders.