A posteriori error estimate for Reissner-Mindlin plates: verification of implementations and numerical testing

Abstract

Work is devoted to analysis of a posteriori error estimate for accuracy control of approximate solutions for problems of Reissner-Mindlin plates bending. The estimate is constructed with the functional approach, which is based on rigorous mathematical grounds, in particular, on methods of functional analysis. It is valid for all conforming approximations of exact solutions, and therefore, it is reliable. The estimate is guaranteed in practical implementations due to robustness of the respective inequality. The above-mentioned properties of the method of error control are very desirable for engineering analysis, where some details might be hidden. Paper investigates two independent implementations of the estimate. Using specially constructed numerical tests, correctness of both implementation algorithms and similarity of the obtained results for all examples are shown. For a wide range of values of plate thicknesses, an overestimation of the true error remains acceptable.

Keywords

• a posteriori error estimate
• finite element method
• reissner – mindlin plate