论文信息 - Adaptive FEM for eigenvalue problems

Adaptive FEM for eigenvalue problems

This paper describes the application of the “dual weighted residual method” for a posteriori error estimation to the Galerkin finite element approximation of elliptic eigenvalue problems. This method employs concepts from optimal control theory to derive identities for the error in the eigenvalues and eigenfunctions in terms of primal and dual residuals. The details can be found in [8].

Rolf Rannacher | Vincent Heuveline

[1] Mats G. Larson,et al. A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems , 2000, SIAM J. Numer. Anal..

[2] Rolf Rannacher,et al. An optimal control approach to a posteriori error estimation in finite element methods , 2001, Acta Numerica.

[3] Rüdiger Verfürth,et al. A posteriori error estimation and adaptive mesh-refinement techniques , 1994 .

[4] M. Chipot. Finite Element Methods for Elliptic Problems , 2000 .

[5] Rolf Rannacher,et al. A posteriori error control for finite element approximations of elliptic eigenvalue problems , 2001, Adv. Comput. Math..

[6] I. Babuska,et al. A‐posteriori error estimates for the finite element method , 1978 .

[7] Rolf Rannacher,et al. A Feed-Back Approach to Error Control in Finite Element Methods: Basic Analysis and Examples , 1996 .