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

Abstract

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.