SERENA: Simulation for the Environment: Reliable and Efficient Numerical Algorithms

output

20142022

H^{1}

and

H (div)

polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions

46 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

collaborating institutions

21 papers

math.NA2022

$h p$ -optimal interior penalty discontinuous Galerkin methods for the biharmonic problem

Zhaonan Dong, Lorenzo Mascotto

We prove $h p$ -optimal error estimates for interior penalty discontinuous Galerkin methods (IPDG) for the biharmonic problem with homogeneous essential boundary conditions. We consi…

math.NA2022

Inexpensive polynomial-degree-robust equilibrated flux a posteriori estimates for isogeometric analysis

Gregor Gantner, Martin Vohralík

We consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimat…

math.NA2022★ 1 cited

Constrained and unconstrained stable discrete minimizations for p-robust local reconstructions in vertex patches in the de Rham complex

T. Chaumont-Frelet, M. Vohralik

We analyze constrained and unconstrained minimization problems on patches of tetrahedra sharing a common vertex with discontinuous piecewise polynomial data of degree p. We show th…

math.NA2021★ 7 cited

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…

math.NA2020★ 1 cited

Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem

Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík

We study extensions of piecewise polynomial data prescribed in a patch of tetrahedra sharing an edge. We show stability in the sense that the minimizers over piecewise polynomial s…

math.NA2020★ 27 cited

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…

math.NA2019★ 1 cited

A variational discrete element method for quasi-static and dynamic elasto-plasticity

Frédéric Marazzato, Alexandre Ern, Laurent Monasse

We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest-order discontinuous Galerkin method parametrized by the cont…

math.NA2019

A quasi-optimal variant of the Hybrid High-Order method for elliptic PDEs with $H^{- 1}$ loads

Alexandre Ern, Pietro Zanotti

Hybrid High-Order methods for elliptic diffusion problems have been originally formulated for loads in the Lebesgue space $L^{2} (Ω)$ . In this paper we devise and analyze a variant th…

math.NA2018★ 18 cited

Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems

Iain Smears, Martin Vohralík

We consider energy norm a posteriori error analysis of conforming finite element approximations of singularly perturbed reaction-diffusion problems on simplicial meshes in arbitrar…

cs.CE2018★ 26 cited

A Hybrid High-Order method for incremental associative plasticity with small deformations

Mickaël Abbas, Alexandre Ern, Nicolas Pignet

We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewi…

math.NA2017★ 23 cited

An adaptive $h p$ -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 $h p$ -finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-…

math.NA2017★ 7 cited

Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods

Thomas Boiveau, Virginie Ehrlacher, Alexandre Ern +1

We devise a space-time tensor method for the low-rank approximation of linear parabolic evolution equations. The proposed method is a stable Galerkin method, uniformly in the discr…

math.NA2017★ 25 cited

A Hybrid High-Order method for highly oscillatory elliptic problems

Matteo Cicuttin, Alexandre Ern, Simon Lemaire

We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are poly…

stat.ML2017★ 1 cited

Optimal Projected Variance Group-Sparse Block PCA

Marie Chavent, Guy Chavent

We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learn…

math.NA2017★ 9 cited

On the notion of boundary conditions in comparison principles for viscosity solutions

Max Jensen, Iain Smears

We collect examples of boundary-value problems of Dirichlet and Dirichlet-Neumann type which we found instructive when designing and analysing numerical methods for fully nonlinear…

math.NA2017★ 46 cited

Stable broken $H^{1}$ and $H (div)$ 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 $H^{1}$ setting, we look for functions…

math.NA2016★ 22 cited

Discrete $p$ -robust $H (div)$ -liftings and a posteriori estimates for elliptic problems with $H^{- 1}$ source terms

Alexandre Ern, Iain Smears, Martin Vohralík

We establish the existence of liftings into discrete subspaces of $H (div)$ of piecewise polynomial data on locally refined simplicial partitions of polygonal/poly…

math.NA2016★ 15 cited

Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method

Iain Smears

The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, it requires the solution of a large nonsymmetric system a…

math.NA2015★ 2 cited

Mollification in strongly Lipschitz domains with application to continuous and discrete De Rham complex

Alexandre Ern, Jean-Luc Guermond

We construct mollification operators in strongly Lipschitz domains that do not invoke non-trivial extensions, are $L^{p}$ stable for any real number $p \in [1, \infty]$ , and commute wit…

math.NA2014★ 15 cited

Nonoverlapping domain decomposition preconditioners for discontinuous Galerkin approximations of Hamilton--Jacobi--Bellman equations

Iain Smears

We analyse a class of nonoverlapping domain decomposition preconditioners for nonsymmetric linear systems arising from discontinuous Galerkin finite element approximation of fully…

math.NA2014★ 34 cited

Discontinuous Galerkin finite element methods for time-dependent Hamilton--Jacobi--Bellman equations with Cordes coefficients

Iain Smears, Endre Süli

We propose and analyse a fully-discrete discontinuous Galerkin time-stepping method for parabolic Hamilton--Jacobi--Bellman equations with Cordes coefficients. The method is consis…

hp-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem