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This paper is concerned with the computable error estimates for theeigenvalue problem which is solved by the general conforming finite elementmethods on the general meshes. Based on the computable error estimate, we cangive an asymptotically lower bound of the general eigenvalues. Furthermore, wealso give a guaranteed upper bound of the error estimates for the firsteigenfunction approximation and a guaranteed lower bound of the firsteigenvalue based on computable error estimator. Some numerical examples arepresented to validate the theoretical results deduced in this paper.

Fully Computable Error Bounds for Eigenvalue Problem