NEw generation MEthods for numerical SImulationS

Project Information

NEMESIS

Grant agreement ID: 101115663

DOI

10.3030/101115663

EC signature date 27 November 2023

Start date 1 January 2024

End date 31 December 2029

Funded under

• European Research Council (ERC)

Total cost

€ 7 818 782,00

EU contribution

€ 7 818 782,00

Coordinated by

UNIVERSITE DE MONTPELLIER
France

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Deliverables

Data Management Plan (1)

Data Management Plan

Publications

Peer reviewed articles (46)

A Discrete Trace Theory for Non-Conforming Polytopal Hybrid Discretisation Methods

Author(s): Badia, Santiago; Droniou, Jerome; Tushar, Jai
Published in: Foundations of Computational Mathematics, 2025, ISSN 1615-3383
Publisher: Springer Nature
DOI: 10.48550/ARXIV.2409.15863

Iterative Solution to the Biharmonic Equation in Mixed Form Discretized by the Hybrid High-Order Method

Author(s): Antonietti, P.F.; Matalon, P.; Verani, M.
Published in: Computers & Mathematics with Applications, 2024, ISSN 1873-7668
Publisher: Elsevier
DOI: 10.1016/J.CAMWA.2024.07.018

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

Author(s): Jérôme Droniou, Marien Hanot, Todd Oliynyk
Published in: Journal of Computational Physics, Issue 529, 2025, ISSN 0021-9991
Publisher: Elsevier BV
DOI: 10.1016/J.JCP.2025.113886

Polytopal mesh agglomeration via geometrical deep learning for three-dimensional heterogeneous domains

Author(s): Paola F. Antonietti; Mattia Corti; Gabriele Martinelli
Published in: Mathematics and Computers in Simulation, 2026, ISSN 1872-7166
Publisher: Elsevier
DOI: 10.48550/ARXIV.2406.10587

MAGNET: an open-source library for mesh agglomeration by graph neural networks

Author(s): Antonietti Paola F., Caldana Matteo, Mazzieri Ilario, Re Fraschini Andrea
Published in: Engineering with Computers, 2025, ISSN 0177-0667
Publisher: Springer Verlag
DOI: 10.1007/S00366-025-02223-Y

A Reynolds-semi-robust and pressure-robust Hybrid High-Order method for the time dependent incompressible Navier–Stokes equations on general meshes

Author(s): Daniel Castanon Quiroz, Daniele A. Di Pietro
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 436, 2025, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2024.117660

"A <mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML"" altimg=""si31.svg""> <mml:mi>p</mml:mi> </mml:math> -adaptive polytopal discontinuous Galerkin method for high-order approximation of brain electrophysiology"

Author(s): Caterina B․ Leimer Saglio, Stefano Pagani, Paola F․ Antonietti
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 446, 2025, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2025.118249

Structure Preserving Polytopal Discontinuous Galerkin Methods for the Numerical Modeling of Neurodegenerative Diseases

Author(s): Mattia Corti; Francesca Bonizzoni; Paola F. Antonietti
Published in: Journal of Scientific Computing, Issue 39, 2024, ISSN 1573-7691
Publisher: Springer Nature
DOI: 10.48550/ARXIV.2308.00547

Pressure and convection robust finite elements for magnetohydrodynamics

Author(s): Beirão da Veiga L.; Dassi F.; Vacca G.
Published in: Numerische Mathematik, 2025, ISSN 0945-3245
Publisher: Springer Nature
DOI: 10.48550/ARXIV.2405.05434

Discontinuous Galerkin approximations of the heterodimer model for protein–protein interaction

Author(s): Paola F. Antonietti, Francesca Bonizzoni, Mattia Corti, Agnese Dall’Olio
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 431, 2025, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2024.117282

Journal of Scientific Computing

Author(s): Paul Houston; Matthew E. Hubbard; Thomas J. Radley; Oliver J. Sutton; Richard S. J. Widdowson
Published in: Journal of Scientific Computing, 2024, ISSN 0885-7474
Publisher: Journal of scientific computing
DOI: 10.48550/ARXIV.2304.09592

Homogeneous Multigrid for Hybrid Discretizations: Application to HHO Methods

Author(s): Di Pietro, Daniele; Dong, Zhaonan; Kanschat, Guido; Matalon, Pierre; Rupp, Andreas
Published in: Numerical Methods for Partial Differential Equations, 2025, ISSN 1098-2426
Publisher: Wiley
DOI: 10.48550/ARXIV.2403.15858

Discovering artificial viscosity models for discontinuous Galerkin approximation of conservation laws using physics-informed machine learning

Author(s): Matteo Caldana, Paola F. Antonietti, Luca Dede'
Published in: Journal of Computational Physics, Issue 520, 2025, ISSN 0021-9991
Publisher: Elsevier BV
DOI: 10.1016/J.JCP.2024.113476

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

Author(s): Jérôme Droniou, Ali Haidar, Roland Masson
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, Issue 59, 2025, ISSN 2822-7840
Publisher: EDP Sciences
DOI: 10.1051/M2AN/2025013

Generalised gradients for virtual elements and applications to a posteriori error analysis

Author(s): Chaumont-Frelet, Théophile; Gedicke, Joscha; Mascotto, Lorenzo
Published in: Mathematics of Computation, 2025, ISSN 1088-6842
Publisher: AMS
DOI: 10.48550/ARXIV.2408.03148

Uniform Poincaré inequalities for the Discrete de Rham complex on general domains

Author(s): Daniele A. Di Pietro, Marien-Lorenzo Hanot
Published in: Results in Applied Mathematics, Issue 23, 2024, ISSN 2590-0374
Publisher: Elsevier BV
DOI: 10.1016/J.RINAM.2024.100496

Polytopal discontinuous Galerkin discretization of brain multiphysics flow dynamics

Author(s): Ivan Fumagalli, Mattia Corti, Nicola Parolini, Paola F. Antonietti
Published in: Journal of Computational Physics, Issue 513, 2025, ISSN 0021-9991
Publisher: Elsevier BV
DOI: 10.1016/J.JCP.2024.113115

Robust discontinuous Galerkin-based scheme for the fully-coupled nonlinear thermo-hydro-mechanical problem

Author(s): Stefano Bonetti, Michele Botti, Paola F Antonietti
Published in: IMA Journal of Numerical Analysis, Issue 45, 2025, ISSN 0272-4979
Publisher: Oxford University Press (OUP)
DOI: 10.1093/IMANUM/DRAE045

Serendipity discrete complexes with enhanced regularity

Author(s): Daniele A. Di Pietro; Marien Hanot; Marwa Salah
Published in: Calcolo, 2025, ISSN 1126-5434
Publisher: Springer Nature
DOI: 10.48550/ARXIV.2407.12625

Exploring tau protein and amyloid-beta propagation: A sensitivity analysis of mathematical models based on biological data

Author(s): Mattia Corti
Published in: Brain Multiphysics, 2024, ISSN 2666-5220
Publisher: ELSEVIER
DOI: 10.1016/J.BRAIN.2024.100098

A Nečas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuška-Aziz inequality

Author(s): Michele Botti, Lorenzo Mascotto
Published in: Journal of Mathematical Analysis and Applications, Issue 545, 2025, ISSN 0022-247X
Publisher: Elsevier BV
DOI: 10.1016/J.JMAA.2024.129159

A structure-preserving LDG discretization of the Fisher–Kolmogorov equation for modeling neurodegenerative diseases

Author(s): Paola F. Antonietti, Mattia Corti, Sergio Gómez, Ilaria Perugia
Published in: Mathematics and Computers in Simulation, Issue 241, 2026, ISSN 0378-4754
Publisher: Elsevier BV
DOI: 10.1016/J.MATCOM.2025.09.006

A high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures

Author(s): Caterina B. Leimer Saglio; Stefano Pagani; Mattia Corti; Paola F. Antonietti
Published in: Computers &amp; Mathematics with Applications, 2026, ISSN 1873-7668
Publisher: Elsevier
DOI: 10.2139/SSRN.4706775

Mathematical Models and Methods in Applied Sciences

Author(s): Lourenço Beirão da Veiga; Daniele A. Di Pietro; Kirubell B. Haile
Published in: Mathematical Models and Methods in Applied Sciences, Issue 34, 2024, ISSN 0218-2025
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0218202524500350

A discrete de Rham discretization of interface diffusion problems with application to the Leaky Dielectric Model

Author(s): Daniele A. Di Pietro, Simon Mendez, Aurelio E. Spadotto
Published in: Journal of Computational Physics, Issue 530, 2025, ISSN 0021-9991
Publisher: Elsevier BV
DOI: 10.1016/J.JCP.2025.113920

Unified Discontinuous Galerkin Analysis of a Thermo/Poro-viscoelasticity Model

Author(s): Stefano Bonetti; Mattia Corti
Published in: Journal of Scientific Computing, 2025, ISSN 1573-7691
Publisher: Springer Nature
DOI: 10.48550/ARXIV.2411.19610

Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system

Author(s): Beirao da Veiga, Lourenco; Hu, Kaibo; Mascotto, Lorenzo
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, 2025, ISSN 2822-7840
Publisher: edp sciences
DOI: 10.48550/ARXIV.2407.19748

A coupled mathematical and numerical model for protein spreading and tissue atrophy applied to Alzheimer’s disease

Author(s): Valentina Pederzoli, Mattia Corti, Davide Riccobelli, Paola F. Antonietti
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 444, 2025, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2025.118118

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

Author(s): Jérôme Droniou, Guillaume Enchéry, Isabelle Faille, Ali Haidar, Roland Masson
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 422, 2024, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2024.116838

Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure

Author(s): Lorenzo Botti, Michele Botti, Daniele Di Pietro, Francesco Massa
Published in: Mathematics of Computation, 2025, ISSN 0025-5718
Publisher: American Mathematical Society (AMS)
DOI: 10.1090/mcom/4049

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

Author(s): Jérôme Droniou, Jia Jia Qian
Published in: Mathematics in Engineering, Issue 6, 2024, ISSN 2640-3501
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI: 10.3934/MINE.2024019

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

Author(s): Jérôme Droniou, Mohamed Laaziri, Roland Masson
Published in: Journal of Computational Physics, Issue 515, 2024, ISSN 0021-9991
Publisher: Elsevier BV
DOI: 10.1016/J.JCP.2024.113295

An exterior calculus framework for polytopal methods

Author(s): Francesco Bonaldi, Daniele Antonio Di Pietro, Jérôme Droniou, Kaibo Hu
Published in: Journal of the European Mathematical Society, 2025, ISSN 1435-9855
Publisher: European Mathematical Society - EMS - Publishing House GmbH
DOI: 10.4171/JEMS/1602

<tt>lymph</tt> : Discontinuous Polytopal Methods for Multi-Physics Differential Problems

Author(s): Paola F. Antonietti, Stefano Bonetti, Michele Botti, Mattia Corti, Ivan Fumagalli, Ilario Mazzieri
Published in: ACM Transactions on Mathematical Software, Issue 51, 2025, ISSN 0098-3500
Publisher: Association for Computing Machinery (ACM)
DOI: 10.1145/3716310

An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact

Author(s): Ilaria Fontana and Daniele A. Di Pietro
Published in: Comput. Meth. Appl. Mech. Engrg., Issue 425, 2024, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2024.116950

A deep learning algorithm to accelerate algebraic multigrid methods in finite element solvers of 3D elliptic PDEs

Author(s): Matteo Caldana, Paola F. Antonietti, Luca Dede'
Published in: Computers &amp; Mathematics with Applications, Issue 167, 2024, ISSN 0898-1221
Publisher: Elsevier BV
DOI: 10.1016/J.CAMWA.2024.05.013

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

Author(s): Daniele A. Di Pietro, Jérôme Droniou, Jia Jia Qian
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 421, 2024, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2024.116765

A Virtual Element method for non-Newtonian pseudoplastic Stokes flows

Author(s): Paola F. Antonietti, Lourenço Beirão da Veiga, Michele Botti, Giuseppe Vacca, Marco Verani
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 428, 2024, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2024.117079

Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix–fracture interfaces

Author(s): Bonaldi, Francesco; Droniou, Jérôme; Masson, Roland
Published in: Mathematics of Computation, Issue 349, 2024, ISSN 1088-6842
Publisher: AMS
DOI: 10.48550/ARXIV.2201.09646

Robust Finite Elements for Linearized Magnetohydrodynamics

Author(s): L. Beirão da Veiga, F. Dassi, G. Vacca
Published in: SIAM Journal on Numerical Analysis, Issue 62, 2024, ISSN 0036-1429
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M1582783

A discrete three-dimensional divdiv complex on polyhedral meshes with application to a mixed formulation of the biharmonic problem

Author(s): Daniele A. Di Pietro, Marien-Lorenzo Hanot
Published in: Mathematical Models and Methods in Applied Sciences, Issue 34, 2024, ISSN 0218-2025
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0218202524500313

Discontinuous Galerkin discretization of coupled poroelasticity–elasticity problems

Author(s): Paola F Antonietti, Michele Botti, Ilario Mazzieri
Published in: IMA Journal of Numerical Analysis, 2024, ISSN 0272-4979
Publisher: Oxford University Press (OUP)
DOI: 10.1093/IMANUM/DRAE093

A Posteriori Error Analysis for a Coupled Stokes-Poroelastic System with Multiple Compartments

Author(s): Ivan Fumagalli; Nicola Parolini; Marco Verani
Published in: Journal of Scientific Computing, 2025, ISSN 1573-7691
Publisher: Springer Nature Link
DOI: 10.48550/ARXIV.2407.09659

Computer Methods in Applied Mechanics and Engineering

Author(s): Paola F. Antonietti; Michele Botti; Alessandra Cancrini; Ilario Mazzieri
Published in: Computer Methods in Applied Mechanics and Engineering, 2025, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.2139/SSRN.5207076

The eXtended virtual element method for elliptic problems with weakly singular solutions

Author(s): Jérôme Droniou, Gianmarco Manzini, Liam Yemm
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 429, 2024, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2024.117129

A Reynolds-SemiRobust Method with Hybrid Velocity and Pressure for the Unsteady Incompressible Navier–Stokes Equations

Author(s): L. Beirão da Veiga, D. A. Di Pietro, J. Droniou, K. B. Haile, T. J. Radley
Published in: SIAM Journal on Numerical Analysis, Issue 63, 2025, ISSN 0036-1429
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/25M1736104

Conference proceedings (1)

Numerical Modelling of Protein Misfolding in Neurodegenerative Diseases: A Computational Study

Author(s): Paola F. Antonietti, Mattia Corti
Published in: Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 1, 2025
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-86173-4_1

Other (2)

Vem++, a C++ library to handle and play with the virtual element method

Author(s): Dassi, F
Published in: Numerical Algorithms, 2024
Publisher: Springer
DOI: 10.21203/RS.3.RS-4432259/V1

SUPG-stabilized time-DG finite and virtual elements for the time-dependent advection–diffusion equation

Author(s): Beirao da Veiga, L; Dassi, F; Gomez Macias, S
Published in: Computer Methods in Applied Mechanics and Engineering, 2024
Publisher: Elsevier
DOI: 10.2139/SSRN.5000036