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We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal testfunctions when applied to solve the Reissner-Mindlin model of plate bending. Weprove that the hybrid variational formulation underlying the DPG method iswell-posed (stable) with a thickness-dependent constant in a norm encompassingthe $L_2$-norms of the bending moment, the shear force, the transversedeflection and the rotation vector. We then construct a numerical solutionscheme based on quadrilateral scalar and vector finite elements of degree $p$.We show that for affine meshes the discretization inherits the stability of thecontinuous formulation provided that the optimal test functions areapproximated by polynomials of degree $p+3$. We prove a theoretical errorestimate in terms of the mesh size $h$ and polynomial degree $p$ anddemonstrate numerical convergence on affine as well as non-affine meshsequences.

Analysis of the Discontinuous Petrov-Galerkin Method with Optimal Test Functions for the Reissner-Mindlin Plate Bending Model