Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems

C. Carstensen, D. Gallistl, M. Schedensack

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)

Abstract

The nonconforming approximation of eigenvalues is of high practical interest because it allows for guaranteed upper and lower eigenvalue bounds and for a convenient computation via a consistent diagonal mass matrix in 2D. The first main result is a comparison which states equivalence of the error of the nonconforming eigenvalue approximation with its best-approximation error and its error in a conforming computation on the same mesh. The second main result is optimality of an adaptive algorithm for the effective eigenvalue computation for the Laplace operator with optimal convergence rates in terms of the number of degrees of freedom relative to the concept of a nonlinear approximation class. The analysis includes an inexact algebraic eigenvalue computation on each level of the adaptive algorithm which requires an iterative algorithm and a controlled termination criterion. The analysis is carried out for the first eigenvalue in a Laplace eigenvalue model problem in 2D.
Original languageEnglish
Pages (from-to)1061-1087
Number of pages27
JournalMathematics of computation
Volume84
Issue number293
DOIs
Publication statusPublished - 2015
Externally publishedYes

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