This paper introduces a novel hybrid high-order (HHO) method to approximate the eigenvalues of a symmetric compact differential operator. The HHO method combines two gradient reconstruction operators by means of a parameter \(0<\alpha <~1\) and introduces a novel cell-based stabilization operator weighted by a parameter \(0<\beta <\infty \). Sufficient conditions on the parameters \(\alpha \) and \(\beta \) are identified leading to a guaranteed lower bound property for the discrete eigenvalues. Moreover optimal convergence rates are established. Numerical studies for the Dirichlet eigenvalue problem of the Laplacian provide evidence for the superiority of the new lower eigenvalue bounds compared to previously available bounds.

本文介绍了一种新的混合高阶 (HHO) 方法来逼近对称紧微分算子的特征值。HHO 方法通过参数\(0<\alpha <~1\)组合了两个梯度重建算子，并引入了一种新的基于单元格的稳定算子，由参数\(0<\beta <\infty \)加权。参数\(\alpha \)和\(\beta \)上的充分条件被确定导致离散特征值有保证的下界属性。此外，建立了最佳收敛速度。拉普拉斯算子的狄利克雷特征值问题的数值研究为新的特征值下界与以前可用的界相比的优越性提供了证据。