Guaranteed lower eigenvalue bounds for the biharmonic equation

@article{Carstensen2014GuaranteedLE,
  title={Guaranteed lower eigenvalue bounds for the biharmonic equation},
  author={Carsten Carstensen and Dietmar Gallistl},
  journal={Numerische Mathematik},
  year={2014},
  volume={126},
  pages={33-51}
}
The computation of lower eigenvalue bounds for the biharmonic operator in the buckling of plates is vital for the safety assessment in structural mechanics and highly on demand for the separation of eigenvalues for the plate’s vibrations. This paper shows that the eigenvalue provided by the nonconforming Morley finite element analysis, which is perhaps a lower eigenvalue bound for the biharmonic eigenvalue in the asymptotic sense, is not always a lower bound. A fully-explicit error analysis of… CONTINUE READING