Abstract
When using finite element and finite difference methods to approximate eigenvalues of 2mth-order elliptic problems, the number of reliable numerical eigenvalues can be estimated in terms of the total degrees of freedom $$N$$ in resulting discrete systems. The truth is worse than what we used to believe in that the percentage of reliable eigenvalues decreases with an increased $$N$$ , even though the number of reliable eigenvalues increases with $$N$$ .
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