A postprocessed error estimate and an adaptive procedure for the semidiscrete finite element method in dynamic analysis

Abstract

Abstract In the paper we present a postprocessed type of a posteriori error estimate and a h ‐version adaptive procedure for the semidiscrete finite element method in dynamic analysis. In space the super‐convergent patch recovery technique is used for determining higher‐order accurate stresses and, thus, a spatial error estimate. In time a postprocessing technique is developed for obtaining a local error estimate for one step time integration schemes (the HHT‐α method). Coupling the error estimate with a mesh generator, a h ‐version adaptive finite element procedure is presented for two‐dimensional dynamic analysis. It updates the spatial mesh and time step automatically so that the discretization errors are controlled within specified tolerances. Numerical studies on different problems are presented for demonstrating the performances of the proposed adaptive procedure.