A POSTERIORI ERROR ESTIMATION BASED ON STRESS SUPER-CONVERGENCE RECOVERY TECHNIQUE FOR GENERALIZED EIGENVALUE PROBLEMS

A posteriori error estimation based on the stress super-convergence recovery technique is proposed. Utilizing the super-convergence characteristics of the finite element solutions at some special points (super-convergence points), the stress solutions at other points in the element can be obtained by interpolating or extrapolating the stress solutions at the super-convergence points in the element and its neighboring elements. The post-processed stress solutions are more precise than the original finite element solutions. The more accurate stress solutions can give an improved strain energy. In the end, the more accurate eigenfrequencies can be obtained through replacing the original strain energy in the Rayleigh quotient by the improved strain energy. The posteriori error estimator is finally achieved by substituting the higher quality eigenfreqencies for the unknown exact solution in the error expression. Numerical examples show that the posterior error estimation proposed in this paper is asymptotically exact. Thus, it can be used as an error estimator for the generalized eigenvalue problems in adaptive finite element analysis.