From Finite Elements to Hybrid High-Order methods

Authors: Di Pietro, Daniele A., Droniou, Jérôme

Subject Terms: Mathematics - Numerical Analysis, 65N30, 65N12

Access URL: http://arxiv.org/abs/2503.00425

A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations

Authors: da Veiga, Lourenço Beirão, Di Pietro, Daniele A., Droniou, Jérôme, Haile, Kirubell B., Radley, Thomas J.

Subject Terms: Mathematics - Numerical Analysis, 65N30, 65N12, 35Q30, 76D07

Access URL: http://arxiv.org/abs/2502.15293

Uniform Poincar\'{e} inequalities for the discrete de Rham complex of differential forms

Authors: Di Pietro, Daniele, Droniou, Jérôme, Hanot, Marien-Lorenzo, Pitassi, Silvano

Subject Terms: Mathematics - Numerical Analysis, 65N30, 65N99, 14F40

Access URL: http://arxiv.org/abs/2501.16116

Reaching the equilibrium: Long-term stable approximations for stochastic non-Newtonian Stokes equations with transport noise

Authors: Droniou, Jerome, Le, Kim-Ngan, Wichmann, Jörn

Subject Terms: Mathematics - Numerical Analysis, Mathematics - Probability, 60H15, 60H35, 60J22, 65C20, 65C30, 65C40, 65M12

Access URL: http://arxiv.org/abs/2412.14316

A discrete trace theory for non-conforming polytopal hybrid discretisation methods

Authors: Badia, Santiago, Droniou, Jerome, Tushar, Jai

Subject Terms: Mathematics - Numerical Analysis

Access URL: http://arxiv.org/abs/2409.15863

Analysis of a VEM-fully discrete polytopal scheme with bubble stabilisation for contact mechanics with Tresca friction

Authors: Droniou, Jérôme, Haidar, Ali, Masson, Roland

Subject Terms: Mathematics - Numerical Analysis

Access URL: http://arxiv.org/abs/2404.03045

The eXtended Virtual Element Method for elliptic problems with weakly singular solutions

Authors: Droniou, Jerome, Manzini, Gianmarco, Yemm, Liam

Subject Terms: Mathematics - Numerical Analysis

Access URL: http://arxiv.org/abs/2402.02902

A polytopal discrete de Rham complex on manifolds, with application to the Maxwell equations

Authors: Droniou, Jérôme, Hanot, Marien, Oliynyk, Todd

Source: J. of Comp. Phys. 529 (2025) 113886

Subject Terms: Mathematics - Numerical Analysis, 65M50, 65M60, 35Q61, 78M10

Access URL: http://arxiv.org/abs/2401.16130

Discretisations of mixed-dimensional Thermo-Hydro-Mechanical models preserving energy estimates

Authors: Droniou, Jerome, Laaziri, Mohamed, Masson, Roland

Subject Terms: Mathematics - Numerical Analysis

Access URL: http://arxiv.org/abs/2401.12342

A pressure-robust Discrete de Rham scheme for the Navier-Stokes equations

Authors: Di Pietro, Daniele A., Droniou, Jerome, Qian, Jia Jia

Subject Terms: Mathematics - Numerical Analysis

Access URL: http://arxiv.org/abs/2401.04456

A bubble VEM-fully discrete polytopal scheme for mixed-dimensional poromechanics with frictional contact at matrix fracture interfaces

Authors: Droniou, Jérôme, Enchéry, Guillaume, Faille, Isabelle, Haidar, Ali, Masson, Roland

Source: Comput. Methods Appl. Mech. Engrg. 422, Paper no. 116838, 25p, 2024

Subject Terms: Mathematics - Numerical Analysis

Access URL: http://arxiv.org/abs/2312.09319

Numerical analysis of the stochastic Stefan problem

Authors: Droniou, Jerome, Khan, Muhammad Awais, Le, Kim Ngan

Subject Terms: Mathematics - Numerical Analysis

Access URL: http://arxiv.org/abs/2306.12668

Two arbitrary-order constraint-preserving schemes for the Yang--Mills equations on polyhedral meshes

Authors: Droniou, Jérôme, Qian, Jia Jia

Subject Terms: Mathematics - Numerical Analysis

Access URL: http://arxiv.org/abs/2306.09751

An exterior calculus framework for polytopal methods

Authors: Bonaldi, Francesco, Di Pietro, Daniele A., Droniou, Jerome, Hu, Kaibo

Subject Terms: Mathematics - Numerical Analysis, 65N30, 65N99, 14F40

Access URL: http://arxiv.org/abs/2303.11093

A polytopal method for the Brinkman problem robust in all regimes

Authors: Di Pietro, Daniele A., Droniou, Jérôme

Subject Terms: Mathematics - Numerical Analysis, 65N30, 65N08, 76S05, 76D07

Access URL: http://arxiv.org/abs/2301.03272

Cohomology of the discrete de Rham complex on domains of general topology

Authors: Di Pietro, Daniele A., Droniou, Jérôme, Pitassi, Silvano

Subject Terms: Mathematics - Numerical Analysis, 65N30, 65N99, 65N12

Access URL: http://arxiv.org/abs/2209.00957

A polyhedral discrete de Rham numerical scheme for the Yang-Mills equations

Authors: Droniou, Jérôme, Oliynyk, Todd A., Qian, Jia Jia

Source: J. Comp. Phys. 478 (2023) 111955

Subject Terms: Mathematics - Numerical Analysis, General Relativity and Quantum Cosmology, 65M12, 65M60, 85C50, 83-08

Access URL: http://arxiv.org/abs/2208.12009

Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method

Authors: Di Pietro, Daniele A., Droniou, Jérôme

Subject Terms: Mathematics - Numerical Analysis, 65N30, 65N99, 65N12, 78A30

Access URL: http://arxiv.org/abs/2203.02939

A hybrid high-order scheme for the stationary, incompressible magnetohydrodynamics equations

Authors: Droniou, Jérôme, Yemm, Liam

Subject Terms: Mathematics - Numerical Analysis, 65N12, 65N15, 65N30, G.1

Access URL: http://arxiv.org/abs/2202.12436

Numerical analysis of the stochastic Stefan problem

Authors: Droniou, Jérôme, Khan, Muhammad Awais, Le, Kim-Ngan

Source: In Computers and Mathematics with Applications 1 November 2024 173:114-140