Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method

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