An oscillation-free adaptive FEM for symmetric eigenvalue problems

作者：Carstensen Carsten^*; Gedicke Joscha

来源：Numerische Mathematik, 2011, 118(3): 401-427.

DOI：10.1007/s00211-011-0367-2

A refined a posteriori error analysis for symmetric eigenvalue problems and the convergence of the first-order adaptive finite element method (AFEM) is presented. The H (1) stability of the L (2) projection provides reliability and efficiency of the edge-contribution of standard residual-based error estimators for P (1) finite element methods. In fact, the volume contributions and even oscillations can be omitted for Courant finite element methods. This allows for a refined averaging scheme and so improves (Mao et al. in Adv Comput Math 25(1-3):135-160, 2006). The proposed AFEM monitors the edge-contributions in a bulk criterion and so enables a contraction property up to higher-order terms and global convergence. Numerical experiments exploit the remaining L (2) error contributions and confirm our theoretical findings. The averaging schemes show a high accuracy and the AFEM leads to optimal empirical convergence rates.

• 出版日期2011-7