On using different recovery procedures for the construction of smoothed stress in finite element method

The performance of three di¤erent stress recovery procedures, namely, the superconvergent patch recovery technique (SPR), the recovery by equilibrium in patches (REP) and a combined method known as the LP procedure is reviewed. Di¤erent order of polynomials and various patch formation strategies have been employed in the numerical studies for the construction of smoothed stress Þelds. Two 2-D elastostatic problems of di¤erent characteristics are used to assess the behaviour of the stress recovery procedures. The numerical results obtained indicate that when the order of polynomial used in the recovery procedure is equal to that of the Þnite element analysis, the behaviours of all three recovery procedures are very similar and all of them are adequate to provide a reliable recovered stress Þeld for error estimation. In case that the order of polynomial of the recovered stress is increased, the LP procedure seems to give a more stable recovery matrix and a more reliable recovered stress Þeld than the REP procedure