Fully discrete DPG methods for the Kirchhoff-Love plate bending model
Provides rigorous numerical analysis for a challenging plate bending model, but is an incremental extension of prior work.
The authors extend the DPG method for Kirchhoff-Love plates to include deflection gradients and prove quasi-optimal convergence for lowest-order schemes with approximated test functions, even for non-convex plates with irregular shear forces.
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, 2018] 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 $L_2$-regular. Numerical results illustrate expected convergence orders.