Conjectured dynamic convergence for mixed finite elements for Mindlin plates

The Mindlin plate problem is formulated with unknowns $e_w$, $\bm{e}_{\theta}$, $\bm{E}_{\kappa}$, and $\bm{e}_{\gamma}$ and corresponding discrete approximations $e_w^h$, $\bm{e}_{\theta}^h$, $\bm{E}_{\kappa}^h$, and $\bm{e}_{\gamma}^h$. The notation $a\lesssim b$ means $a\leq Cb$, where $C$ depends only on the true solution and the final time.

Dynamic convergence conjecture. Assuming a smooth solution to the Mindlin plate problem, the error estimates

$$\lVert e_w-e_w^h\rVert_{L^{\infty}(L^2)}\lesssim h^k,$$ $$\lVert\bm{e}_{\theta}-\bm{e}_{\theta}^h\rVert_{L^{\infty}(L^2)}\lesssim h^k,$$ $$\lVert\bm{E}_{\kappa}-\bm{E}_{\kappa}^h\rVert_{L^{\infty}(L^2)}\lesssim h^k,$$ $$\lVert\bm{e}_{\gamma}-\bm{e}_{\gamma}^h\rVert_{L^{\infty}(L^2)}\lesssim h^k$$

should hold.

These estimates conjecturally extend convergence results for the corresponding static problem to the dynamical Mindlin plate problem. The paper provides the mixed finite-element formulation but does not establish the stated error bounds.