High-accuracy approximations for eigenvalue problems by the Carey non-conforming finite element

In this paper the Carey non-conforming finite element is considered for sol ving eigenvalue problems of the second-order elliptic operator. Based on an interpolation postprocessing, high-accuracy estimates of both eigenfunctio ns and eigenvalues are obtained: parallel to Pi(2h)(2)u(h) - u parallel to(1) less than or equal to Ch(2)par allel to u parallel to(3) 0 less than or equal to <(lambda)over cap>(h) - lambda less than or equal t o Ch(4)parallel to u parallel to(3)(2) Here, Pi(2h)(2) is an interpolation operator, (lambda, u) and (lambda(h), u (h)) are eigenpairs for the exact problem and its Carey element approximati ons, respectively, and lambda(h) is defined by the Rayleigh ratio of Pi(2h) (2)u(h). Copyright (C) 1999 John Wiley & Sons, Ltd.