We present an a posteriori error analysis for the postprocessed mixed interpolated tensorial components (MITC) finite element methods approximating the solution of the Reissner--Mindlin plate bending problem. We first prove a new a priori error estimate by utilizing the results for the postprocessing method. Then we introduce a residual-based a posteriori error estimator and prove its reliability and efficiency with techniques similar to those recently used for the original MITC elements. The basic features of the error estimator in adaptive computations are illustrated by a series of numerical tests for a triangular low order element.
A Posteriori Error Analysis for the Postprocessed MITC Plate Elements / L. Beirao da Veiga, J. Niiranen, R. Stenberg. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 51:1(2013), pp. 1-23. [10.1137/11085640X]