Rigorous and fully computable a posteriori error bounds for eigenfunctions
| Type of publication: | Misc |
| Citation: | |
| Publication status: | Submitted |
| Year: | 2019 |
| Abstract: | Guaranteed a posteriori estimates on the error of approximate eigenfunctions in both energy and L2 norms are derived for the Laplace eigenvalue problem. The problem of ill-conditioning of eigenfunctions in case of tight clusters and multiple eigenvalues is solved by estimat- ing the directed distance between the spaces of exact and approximate eigenfunctions. The error estimates for approximate eigenfunctions are based on rigorous lower and upper bounds on eigenvalues. Such eigenvalue bounds can be computed for example by the nite element method along with the recently developed explicit error estimation [24] and the Lehmann{Goerisch method. The eciency of the derived error bounds for eigenfunctions is illustrated by numerical examples. |
| Preprint project: | NCMM |
| Preprint year: | 2019 |
| Preprint number: | 02 |
| Preprint ID: | NCMM/2019/02 |
| Keywords: | |
| Authors | |
| Added by: | [MB] |
| Total mark: | 0 |
|
Attachments
|
|
|
|
|
Notes
|
|
|
|
|
|
Topics
|
|
