Superconvergent Patch Recovery in Problems of Mixed Form

Abstract

SUMMARYThe superconvergent patch recovery (SPR technique) has been shown to be an eective postprocessing procedure in which an improved solution is obtained based on the original ®nite element solution. The technique was applied to second order problems with success, but the method has not yet been studied on problems posed in mixed form. This paper demonstrates that the technique can be applied to beam and plate bending problems, characterized by fourth order dierential equations. The dierential equation is here written as two coupled dierential equations of second order leading to a mixed ®nite element procedure based on approximations of the moment and displacement ®elds. Two elements of mixed type are handled, namely a triangular plate element with constant moment ®eld and a rectangular element with linearly varying bending moments. Numerical examples are given to show that the postprocessed solution is more accurate and has a higher rate of convergence.