8 papers · 1 filter
A quasi-interpolation operator yielding fully computable error bounds
T. Chaumont-Frelet, M. Vohralik
We design a quasi-interpolation operator from the Sobolev space to its finite-dimensional finite element subspace formed by piecewise polynomials on a simplicial mesh wi…
Local L2-bounded commuting projections using discrete local problems on Alfeld splits
Alexandre Ern, Johnny Guzman, Pratyush Potu +1
We construct projections onto the classical finite element spaces based on Lagrange, Nédélec, Raviart-Thomas, and discontinuous elements on shape-regular simplicial meshes. Our pro…
A-posteriori-steered -robust multigrid and domain decomposition methods with optimal step-sizes for mixed finite element discretizations of elliptic problems
Ani Miraçi, Jan Papež, Martin Vohralík +1
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite e…
A posteriori error estimates for the Richards equation
K. Mitra, M. Vohralík
The Richards equation is commonly used to model the flow of water and air through soil, and it serves as a gateway equation for multiphase flows through porous media. It is a nonli…
On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation
T. Chaumont-Frelet, A. Ern, M. Vohralík
We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilib…
Guaranteed a posteriori bounds for eigenvalues and eigenvectors: multiplicities and clusters
Eric Cancès, Geneviève Dusson, Yvon Maday +2
This paper presents a posteriori error estimates for conforming numerical approximations of eigenvalue clusters of second-order self-adjoint elliptic linear operators with compact…