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In this paper, we study an adaptive finite element method for multipleeigenvalue problems of a class of second order elliptic equations. By usingsome eigenspace approximation technology and its crucial property which is alsopresented in this paper, we extend the results in \cite{dai-xu-zhou08} tomultiple eigenvalue problems, we obtain both convergence rate and quasi-optimalcomplexity of the adaptive finite element eigenvalue approximation.

Convergence Rate and Quasi-Optimal Complexity of Adaptive Finite Element Computations for Multiple Eigenvalues