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Enhancing finite element approximation for eigenvalue problems by projection method. (English) Zbl 1253.74107
Summary: We establish the superconvergence and the related recovery type a posteriori error estimators based on projection method for finite element approximation of the elliptic eigenvalue problems. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The results are based on some regularity assumption for the elliptic problem, and are applicable to the finite element approximations of self-adjoint elliptic eigenvalue problems with general quasi-regular partitions. Therefore, the result of this paper can be employed to provide useful a posteriori error estimators in adaptive finite element computation under unstructured meshes.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R99 Fracture and damage
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K20 Plates
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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