A posteriori error control for finite element approximations of elliptic eigenvalue problems. Heuveline, V & Rannacher, R ADVANCES IN COMPUTATIONAL MATHEMATICS, 15:107--138, 2001.
A posteriori error control for finite element approximations of elliptic eigenvalue problems [link]Paper  doi  abstract   bibtex   
We develop a new approach to a posteriori error estimation for Galerkin finite element approximations of symmetric and nonsymmetric elliptic eigenvalue problems, The idea is to embed the eigenvalue approximation into the general framework of Galerkin methods for nonlinear variational equations. In this context residual-based a posteriori error representations are available with explicitly given remainder terms. The careful evaluation of these error representations for the concrete situation of an eigenvalue problem results in a posteriori error estimates for the approximations of eigenvalues as well as eigenfunctions. These suggest local error indicators that are used in the mesh refinement process.
@article{ Heuveline2001,
  abstract = {We develop a new approach to a posteriori error estimation for Galerkin finite element approximations of symmetric and nonsymmetric elliptic eigenvalue problems, The idea is to embed the eigenvalue approximation into the general framework of Galerkin methods for nonlinear variational equations. In this context residual-based a posteriori error representations are available with explicitly given remainder terms. The careful evaluation of these error representations for the concrete situation of an eigenvalue problem results in a posteriori error estimates for the approximations of eigenvalues as well as eigenfunctions. These suggest local error indicators that are used in the mesh refinement process.},
  author = {Heuveline, V and Rannacher, R},
  doi = {10.1023/A:1014291224961},
  issn = {1019-7168},
  journal = {ADVANCES IN COMPUTATIONAL MATHEMATICS},
  keywords = {A-POSTERIORI,a posteriori error estimate,eigenvalue problem,finite element method,mesh adaptation},
  pages = {107--138},
  title = {{A posteriori error control for finite element approximations of elliptic eigenvalue problems}},
  url = {http://apps.webofknowledge.com/full_record.do?product=WOS\&search_mode=Refine\&qid=16\&SID=Y2kF2E94IKI7ENOMD@O\&page=1\&doc=1\&cacheurlFromRightClick=no},
  volume = {15},
  year = {2001}
}
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