8 citations · 8 across the 3 of their papers we have counts for
8 papers · 1 filter
Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence
Zhaonan Dong, Alexandre Ern, Jean-Luc Guermond
We estimate best-approximation errors using vector-valued finite elements for fields with low regularity in the scale of fractional-order Sobolev spaces. By assuming additionally t…
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…
Artificial compressibility methods for the incompressible Navier-Stokes equations using lowest-order face-based schemes on polytopal meshes
Riccardo Milani, Jérôme Bonelle, Alexandre Ern
We investigate artificial compressibility (AC) techniques for the time discretization of the incompressible Navier-Stokes equations. The space discretization is based on a lowest-o…
SoftFEM: revisiting the spectral finite element approximation of second-order elliptic operators
Quanling Deng, Alexandre Ern
We propose, analyze mathematically, and study numerically a novel approach for the finite element approximation of the spectrum of second-order elliptic operators. The main idea is…
An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics
Frédéric Marazzato, Alexandre Ern, Christian Mariotti +1
We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is base…
Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron
Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
We prove that the minimizer in the Nédélec polynomial space of some degree p > 0 of a discrete minimization problem performs as well as the continuous minimizer in H(curl), up to a…