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06/22/2023
Numerical analysis of the stochastic Stefan problem
The gradient discretisation method (GDM) – a generic framework encompass...
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06/16/2023
Two arbitrary-order constraint-preserving schemes for the Yang–Mills equations on polyhedral meshes
Two numerical schemes are proposed and investigated for the Yang–Mills e...
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03/20/2023
An exterior calculus framework for polytopal methods
We develop in this work the first polytopal complexes of differential fo...
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01/09/2023
A polytopal method for the Brinkman problem robust in all regimes
In this work we develop a discretisation method for the Brinkman problem...
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09/02/2022
Cohomology of the discrete de Rham complex on domains of general topology
In this work we prove that, for a general polyhedral domain of $\Real^3$...
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08/25/2022
A polyhedral discrete de Rham numerical scheme for the Yang-Mills equations
We present a discretisation of the 3+1 formulation of the Yang-Mills equ...
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03/06/2022
Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method
In this work we investigate from a broad perspective the reduction of de...
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02/25/2022
A Hybrid High-Order scheme for the stationary, incompressible magnetohydrodynamics equations
We propose and analyse a hybrid high-order (HHO) scheme for stationary i...
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01/24/2022
Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix-fracture interfaces
We present a complete numerical analysis for a general discretization of...
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12/29/2021
A fully discrete plates complex on polygonal meshes with application to the Kirchhoff-Love problem
In this work we develop a novel fully discrete version of the plates com...
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12/17/2021
Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
This paper contains two major contributions. First we derive, following ...
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10/01/2021
A cost-effective nonlinear extremum-preserving finite volume scheme for highly anisotropic diffusion on Cartesian grids, with application to radiation belt dynamics
We construct a new nonlinear finite volume (FV) scheme for highly anisot...
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09/21/2021
Conditioning of a Hybrid High-Order scheme on meshes with small faces
We conduct a condition number analysis of a Hybrid High-Order (HHO) sche...
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09/20/2021
Energy-stable discretization of two-phase flows in deformable porous media with frictional contact at matrix-fracture interfaces
We address the discretization of two-phase Darcy flows in a fractured an...
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05/25/2021
A DDR method for the Reissner-Mindlin plate bending problem on polygonal meshes
In this work we propose a discretisation method for the Reissner–Mindlin...
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02/12/2021
Robust Hybrid High-Order method on polytopal meshes with small faces
We design a Hybrid High-Order (HHO) scheme for the Poisson problem that ...
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01/13/2021
An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency
In this paper we prove a complete panel of consistency results for the d...
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01/13/2021
An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency
In this paper we present a novel arbitrary-order discrete de Rham (DDR) ...
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12/09/2020
Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems
We derive novel error estimates for Hybrid High-Order (HHO) discretizati...
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11/11/2020
Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces
We consider a two-phase Darcy flow in a fractured and deformable porous ...
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07/14/2020
Non-conforming finite elements on polytopal meshes
In this work we present a generic framework for non-conforming finite el...
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05/14/2020
An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence
In this work, we develop a discretisation method for the mixed formulati...
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04/25/2020
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray-Lions operator
The gradient discretisation method (GDM) is a generic framework, coverin...
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04/21/2020
Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media
We consider a two-phase Darcy flow in a fractured porous medium consisti...
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04/21/2020
Hessian discretisation method for fourth order semi-linear elliptic equations: applications to the von Kármán and Navier–Stokes models
This paper deals with the Hessian discretisation method (HDM) for fourth...
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03/20/2020
Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations
Gradient schemes is a framework that enables the unified convergence ana...
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01/29/2020
Interplay between diffusion anisotropy and mesh skewness in Hybrid High-Order schemes
We explore the effects of mesh skewness on the accuracy of standard Hybr...
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01/07/2020
Numerical solution of a two dimensional tumour growth model with moving boundary
We consider a biphasic continuum model for avascular tumour growth in tw...
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11/09/2019
Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
In this work, merging ideas from compatible discretisations and polyhedr...
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10/17/2019
Convergence analysis of a numerical scheme for a tumour growth model
We consider a one-spatial dimensional tumour growth model that consists ...
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08/16/2019
An efficient implementation of mass conserving characteristic-based schemes in 2D and 3D
In this paper, we develop the ball-approximated characteristics (B-char)...
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07/13/2017