Uniform interior error estimates for the Reissner-Mindlin plate model

Abstract

Abstract. Interior error estimates are derived for the solution of the ReissnerMindlin plate model discretized by mixed-interpolated elements. Precisely, it is shown that the error in an interior domain can be estimated by the sum of two terms: the first has the best order of accuracy that is possible locally for the finite element spaces used, the second is a weak norm of the error on a slightly larger domain (this term measures the effects from outside of this domain). The analysis is based on some abstract properties enjoyed by the finite element spaces considered.

Locking-free finite element methods for shells

“…In any case, Theorem 5 shows that the finite element solution provides the best approximation that the regularity of the solution allows, uniformly with respect to t. Moreover, when the presence of boundary layers precludes the optimal rates of convergence uniform in t, it is still possible that such convergence occurs on interior subdomains. Interior convergence results of this sort have been established for some Reissner-Mindlin plate elements in [10] and [13]. We also mention that by analyzing more carefully the norm ||| · |||, instead of simply bounding it by the L 2 norm, the norm on the solution which appears on the right-hand side of (17) can probably be replaced with a weaker one (but generally not by one that is bounded uniformly in t).…”

Local error estimates for finite element discretization of the Stokes equations

“…Although the gênerai approach is not new, there are a number of significant difficulties which anse for the Stokes System that are not present in previous works. Recently, Lucia Gastaldi [7] obtained interior error estimâtes for some finite element methods for the Reissner-Mindlin plate model. This work is related to local error analysis of the Stokes équations since the Reissner-Mindlin model can be reformulated as a decoupled System of two Laplace équations and a perturbed Stokes system.…”

A Simple Strain Recovery based A-posteriori Error Estimator for Laminated Composite Plates

“…in the absence of boundary layer effects, and for a fixed d (see [18] for a detailed proof on convergence of local error for isotropic plates). Thus, if the finite element solution is obtained over the same mesh using (p+1) order elements, the error e p+1 = u − u FE p+1 in the finite element solution u FE p+1 satisfies :…”