It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility condition (inclusion of kernels) of the mixed scheme and on local constants related to compact embeddings, which are often known explicitly. Applications include scalar second-order elliptic operators, linear elasticity, and the Steklov eigenvalue problem.

翻译：针对与偏微分算子相关的对称正定特征值问题，本文展示了混合有限元方法如何提供有保证的下特征值界限。该方法基于混合格式的经典相容性条件（核的包含关系）以及通常已知显式表达的紧嵌入相关局部常数。其应用涵盖标量二阶椭圆算子、线弹性问题以及Steklov特征值问题。