Implementation and analysis of error estimates for hp MITC finite elements of Reissner–Mindlin plates

This thesis concerns a priori and a posteriori error estimates of hp MITC finite elements for Reissner–Mindlin plates. First, we recall the theory for the Reissner–Mindlin plate model, starting from the principle of virtual work resulting in the strong form of the partial differential equations and boundary conditions. Second, we derive the standard form finite element method for the Reissner–Mindlin plate problem. After a concise discussion in regard to the so-called shear locking effect, the non-standard MITC finite element method is presented. Third, a priori and a posteriori error analysis are reviewed briefly, and the convergence results as well as error estimators for the MITC plate elements are introduced. Eventually, the MITC finite element method for Reissner–Mindlin plates is implemented into a high-order finite element solver with C++ programming language. The method is verified by conducting an a priori error analysis using hp refinements. Thereafter, the a posteriori error estimators of the standard and MITC finite element method are implemented into the solver, and the behaviour of the estimators and their contribution to the global error estimator are studied. The provided results are in accordance with the theory. The a priori error estimators show the advantage of the MITC finite element over the standard finite element method in the terms of stability and convergence rate in the presence of the shear locking effect with thin plates. The corresponding convergence rates of the a posteriori estimators guarantee a basis for efficient adaptive refinements. Moreover, estimators are found capable of detecting a boundary layer in the case of a free boundary plate. Hence, it might be possible to use them for hp-refinement