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


A posteriori error estimate for accuracy control of approximate solutions for the problem of Reissner – Mindlin plates bending has been analyzed in the paper. The estimate was constructed using the functional approach 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 robust. The estimate is guaranteed in practical implementations due to reliability of the respective inequality. The above-mentioned properties of the method of error control are very desirable for engineering analysis, where some details of computations might be hidden. Our paper investigated 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 were shown. An overestimation of the true error was established to remain acceptable for a wide range of plate thickness values.