Stress recovery and error estimation for the scaled boundary finite-element method

The scaled boundary nite-element method is a novel semi-analytical technique, combining the advantages of the nite element and the boundary element methods with unique properties of its own. This paper develops a stress recovery procedure based on a modal interpretation of the scaled boundary nite-element method solution process, using the superconvergent patch recovery technique. The recovered stresses are superconvergent, and are used to calculate a recovery-type error estimator. A key feature of the procedure is the compatibility of the error estimator with the standard recovery-type nite element estimator, allowing the scaled boundary nite-element method to be compared directly with the nite element method for the rst time. A plane strain problem for which an exact solution is available is presented, both to establish the accuracy of the proposed procedures, and to demonstrate the e ectiveness of the scaled boundary nite-element method. The scaled boundary nite-element estimator is shown to predict the true error more closely than the equivalent nite element error estimator. Unlike their nite element counterparts, the stress recovery and error estimation techniques work well with unbounded domains and stress singularities