In this paper, we study the approximation of eigenvalues arising from the mixed Hellinger–Reissner elasticity problem by using a simple finite element introduced recently by one of the authors. We prove that the method converges when a residual type error estimator is considered and that the estimator decays optimally with respect to the number of degrees of freedom. A postprocessing technique originally proposed in a different context is discussed and tested numerically.

中文翻译：

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Hellinger-Reissner 弹性混合特征值问题的自适应有限元方案

在本文中，我们使用作者之一最近引入的简单有限元研究了由混合 Hellinger-Reissner 弹性问题产生的特征值的近似值。我们证明，当考虑残差类型误差估计量时，该方法收敛，并且估计量相对于自由度数以最佳方式衰减。最初在不同上下文中提出的后处理技术进行了讨论和数值测试。