This paper introduces fully computable two-sided bounds on the eigenvalues of the Laplace
operator on arbitrarily coarse meshes based on some approximation of the corresponding …

The computation of lower eigenvalue bounds for the biharmonic operator in the buckling of
plates is vital for the safety assessment in structural mechanics and highly on demand for the …

This paper derives a posteriori error estimates for conforming numerical approximations of
the Laplace eigenvalue problem with a homogeneous Dirichlet boundary condition. In …

Nearly all inf-sup stable mixed finite elements for the incompressible Stokes equations relax
the divergence constraint. The price to pay is that a priori estimates for the velocity error …

A posteriori error estimates are an important tool to bound discretization errors in terms of
computable quantities avoiding regularity conditions that are often difficult to establish. For …

The lowest-order nonconforming virtual element extends the Morley triangular element to
polygons for the approximation of the weak solution to the biharmonic equation. The abstract …

In this paper, we introduce two one-parameter families of quadratic polynomial enrichments
designed to enhance the accuracy of the classical Crouzeix–Raviart finite element. These …

The known a posteriori error analysis of hybrid high-order methods treats the stabilization
contribution as part of the error and as part of the error estimator for an efficient and reliable …

This paper develops a general framework for a posteriori error estimates in numerical
approximations of the Laplace eigenvalue problem, applicable to all standard numerical …

This paper presents a posteriori error estimates for conforming numerical approximations of
eigenvalue clusters of second-order self-adjoint elliptic linear operators with compact …