47 citations · 202 across the 12 of their papers we have counts for
13 papers
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…
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver
Alexander Haberl, Dirk Praetorius, Stefan Schimanko +1
We consider a second-order elliptic boundary value problem with strongly monotone and Lipschitz-continuous nonlinearity. We design and study its adaptive numerical approximation in…
Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal approximation estimates in
Alexandre Ern, Thirupathi Gudi, Iain Smears +1
Given an arbitrary function in H(div), we show that the error attained by the global-best approximation by H(div)-conforming piecewise polynomial Raviart-Thomas-Nédélec elements un…
An adaptive -refinement strategy with computable guaranteed bound on the error reduction factor
Patrik Daniel, Alexandre Ern, Iain Smears +1
We propose a new practical adaptive refinement strategy for -finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-…
Equilibrated flux a posteriori error estimates in -norms for high-order discretizations of parabolic problems
Alexandre Ern, Iain Smears, Martin Vohralik
We consider the a posteriori error analysis of fully discrete approximations of parabolic problems based on conforming -finite element methods in space and an arbitrary order d…
Stable broken and polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions
Alexandre Ern, Martin Vohralík
We study extensions of piecewise polynomial data prescribed on faces and possibly in elements of a patch of simplices sharing a vertex. In the setting, we look for functions…
Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems
Alexandre Ern, Iain Smears, Martin Vohralík
We consider the a posteriori error analysis of approximations of parabolic problems based on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high…
Discrete -robust -liftings and a posteriori estimates for elliptic problems with source terms
Alexandre Ern, Iain Smears, Martin Vohralík
We establish the existence of liftings into discrete subspaces of of piecewise polynomial data on locally refined simplicial partitions of polygonal/poly…