A posteriori error estimators for convection--diffusion eigenvalue problems

A posteriori error estimators for convection–diffusion eigenvalue model problems are discussed in Heuveline and Rannacher (2001) [17] in the context of the dual-weighted residual method (DWR). This paper directly addresses the variational formulation rather than the non-linear ansatz of Becker and Rannacher for some convection–diffusion model problem and presents a posteriori error estimators for the eigenvalue error based on averaging techniques. Two different postprocessing techniques attached to the DWR paradigm plus two new dual-weighted a posteriori error estimators are also presented. The first new estimator utilises an auxiliary Raviart–Thomas mixed finite element method and the second exploits an averaging technique in combination with ideas of DWR. The six a posteriori error estimators are compared in three numerical examples and illustrate reliability and efficiency and the dependence of generic constants on the size of the eigenvalue or the convection coefficient.

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