Quasi‐optimality of the adaptive finite element method for the eigenvalue problem arising from the vibration frequencies of the cavity flow

In this article, we present a posteriori error analysis for the regularization formulation of the eigenvalue problem arising from the vibration frequencies of the cavity flow. The quasi‐optimality of the adaptive finite element method is also proved for the single eigenvalues under the Dörfler's marking strategy without marking the oscillation terms and enforcing the so‐called interior node property. Numerical examples illustrate the quasi‐optimality of the adaptive finite element method. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 900–922, 2015