A posteriori error estimation in finite element analysis of plate structures

A posteriori error estimation is an important tool in finite element software development, since it allows to verify and validate the finite element simulations. An efficient and practical way to derive a posteriori error estimators is offered by recovery procedures, which estimate the error by comparing the original finite element solution with the recovered one. The major steps forward in using recovery procedures were made with the Superconvergent Patch Recovery (SPR) and the Recovery by Equilibrium in Patches (REP) procedures [1,2], both successfully applied to plate problems in [3]. Recently, a new superconvergent procedure called Recovery by Compatibility in Patches (RCP) has been proposed by one of the authors [4] and shown to provide an excellent basis for error estimation in 2D problems [5]. Within this context, the present paper aims at presenting an extension of the RCP-based error estimation to Reissner-Mindlin plates finite element analysis. The basic idea is to recover stress resultants by enforcing compatibility over patches of elements. Displacements computed by the finite element analysis are prescribed on the boundary of the patch, and improved stress resultants are computed by minimizing the complementary energy of such a sub-model. The resulting procedure is simple, efficient, numerically stable and does not need any knowledge of superconvergent points. Some numerical examples are given. References: 1. O.C. Zienkiewicz, J.Z. Zhu, “The superconvergent patch recovery and a posteriori error estimates. Part I: The recovery technique”, International Journal for Numerical Methods in Engineering, v. 33, p. 1331-1364, 1992. 2. B. Boroomand, O.C. Zienkiewicz, “An improved REP recovery and the effectivity robustness test”, International Journal for Numerical Methods in Engineering, v. 40, p. 3247-3277, 1997. 3. B. Boroomand, M. Ghaffarian, O.C. Zienkiewicz, “On application of two superconvergent recovery procedures to plate problems”, International Journal for Numerical Methods in Engineering, v. 61, p. 1644-1673, 2004. 4. F. Ubertini, “Patch recovery based on complementary energy”, International Journal for Numerical Methods in Engineering, v. 59, p. 1501-1538, 2004. 5. A. Benedetti, S. de Miranda, F. Ubertini, “A posteriori error estimation based on the superconvergent Recovery by Compatibility in Patches”, International Journal for Numerical Methods in Engineering, in press