74 citations · 654 across the 39 of their papers we have counts for
6 papers · 1 filter
Hybrid high-order method for singularly perturbed fourth-order problems on curved domains
Zhaonan Dong, Alexandre Ern
We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising th…
Hybrid high-order methods. A primer with application to solid mechanics
Matteo Cicuttin, Alexandre Ern, Nicolas Pignet
This book is organized into eight chapters. The first three gently introduce the basic principles of hybrid high-order methods on a linear diffusion problem, the key ideas underlyi…
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…
Hybrid high-order and weak Galerkin methods for the biharmonic problem
Zhaonan Dong, Alexandre Ern
We devise and analyze two hybrid high-order (HHO) methods for the numerical approximation of the biharmonic problem. The methods support polyhedral meshes, rely on the primal formu…
Quasi-static crack propagation with a Griffith criterion using a variational discrete element method
Frédéric Marazzato, Alexandre Ern, Laurent Monasse
A variational discrete element method is applied to simulate quasi-static crack propagation. Cracks are considered to propagate between the mesh cells through the mesh facets. The…