A posteriori and a priori error analysis for finite element approximations of self-adjoint elliptic eigenvalue problems. (English) Zbl 0974.65100
A new error analysis for finite element approximations of selfadjoint elliptic eigenvalue problems is presented. The analysis consists of three steps. First a posteriori estimates for the error in the approximate eigenvalues and eigenfunctions are proved. Next an a priori estimate of the residual in terms of derivatives of the exact eigenfunctions and the mesh size is derived. Finally precise a priori estimates by combination of the a posteriori error estimates with the a priori residual estimates are obtained. The analysis shows that the a posteriori estimates are optimal and may be used for quantative error estimation and design of adaptive algorithms.
Reviewer: Plamen Yordanov Yalamov (Russe)
MSC:
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35P15 | Estimates of eigenvalues in context of PDEs |
