Fully discrete DPG methods for the Kirchhoff-Love plate bending model

We extend the analysis and discretization of the Kirchhoff-Love plate bending problem from Führer et al. (in press) in two aspects. First, we present a well-posed formulation and quasi-optimal DPG discretization that include 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.