Convergence and optimal complexity of adaptive finite element eigenvalue computations. (English) Zbl 1159.65090
The paper deals with an adaptive finite element method for elliptic eigenvalue problems. The authors establish a relationship between the elliptic eigenvalue approximation and the associated boundary value approximation in order to establish a posteriori error estimators for the finite element eigenvalue solutions. After the adaptive algorithm for the finite element eigenvalues is designed, the convergence and optimal complexity of the adaptive finite element eigenvalue computation are proved. Several numerical experiments, supporting the theory, are presented.
Reviewer: Adrian Carabineanu (Bucureşti)
MSC:
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65Y20 | Complexity and performance of numerical algorithms |
Keywords:
elliptic boundary value problem; adaptive finite element method; elliptic eigenvalue problems; a posteriori error estimators; algorithm; convergence; optimal complexity; numerical experimentsReferences:
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