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Forthcoming articles

ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN) gives online access to unedited preprint version of accepted papers, ahead of publication. This online version does not take into account corrections made during production process.

Online access to PDF files is granted to subscribers.

A posteriori error control for a finite volume scheme for a cross-diffusion model of ion transport

Arne Berrens and Jan Giesselmann
ESAIM: M2AN, Forthcoming article
Received: 21 July 2025 / Revised: 19 January 2026 / Accepted: 28 January 2026
DOI: https://doi.org/10.1051/m2an/2026014

Self-regulated biological transportation structures with general entropy dissipation: 2D case and leaf-shaped domain

Clarissa Astuto, Peter Markowich, Simone Portaro and Giovanni Russo
ESAIM: M2AN, Forthcoming article
Received: 20 October 2024 / Revised: 11 August 2025 / Accepted: 27 January 2026
DOI: https://doi.org/10.1051/m2an/2026011

Nonsmooth data error estimates for exponential Runge–Kutta methods and applications to split exponential integrators

Qiumei Huang, Alexander Ostermann and Gangfan Zhong
ESAIM: M2AN, Forthcoming article
Received: 07 July 2025 / Revised: 12 November 2025 / Accepted: 21 January 2026
DOI: https://doi.org/10.1051/m2an/2026009

A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes

Thomas Borsoni, Laurent Boudin, Julien Mathiaud and Francesco Salvarani
ESAIM: M2AN, Forthcoming article
Received: 11 June 2025 / Revised: 02 December 2025 / Accepted: 19 January 2026
DOI: https://doi.org/10.1051/m2an/2026008

Enriching continuous Lagrange finite element approximation spaces using neural networks

Hélène Barucq, Michel Duprez, Florian Faucher, Emmanuel Franck, Frédérique Lecourtier, Vanessa Lleras, Victor Michel-Dansac and Nicolas Victorion
ESAIM: M2AN, Forthcoming article
Received: 14 February 2025 / Revised: 14 December 2025 / Accepted: 15 January 2026
DOI: https://doi.org/10.1051/m2an/2026007

Nitsche stabilized virtual element approximations for a Brinkman problem with mixed boundary conditions

David Mora, Jesus Vellojin and Nitesh Verma
ESAIM: M2AN, Forthcoming article
Received: 11 June 2024 / Revised: 07 December 2025 / Accepted: 13 January 2026
DOI: https://doi.org/10.1051/m2an/2026005

A generalized framework for higher-order Localized Orthogonal Decomposition methods

Moritz Hauck, Alexei Lozinski and Roland Maier
ESAIM: M2AN, Forthcoming article
Received: 30 July 2025 / Revised: 02 December 2025 / Accepted: 13 January 2026
DOI: https://doi.org/10.1051/m2an/2026006

High order Asymptotic-Preserving penalized numerical schemes for the Euler-Poisson system in the quasineutral limit

Nicolas Crouseilles, Giacomo Dimarco and Saurav Samantaray
ESAIM: M2AN, Forthcoming article
Received: 30 December 2024 / Revised: 10 December 2025 / Accepted: 08 January 2026
DOI: https://doi.org/10.1051/m2an/2026004

Time discretization in convected linearized thermo-visco-elastodynamics at large displacements.

Tomas Roubicek
ESAIM: M2AN, Forthcoming article
Received: 19 April 2025 / Revised: 07 December 2025 / Accepted: 08 January 2026
DOI: https://doi.org/10.1051/m2an/2026003

Asymptotic analysis of high order IMEX-RK methods for ES-BGK model at Navier-Stokes level

Sebastiano Boscarino and Seung Yeon Cho
ESAIM: M2AN, Forthcoming article
Received: 22 August 2025 / Revised: 23 December 2025 / Accepted: 06 January 2026
DOI: https://doi.org/10.1051/m2an/2026002

Two-scale integrators with high accuracy and long-time conservations for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime

Bin Wang, Zhen Miao and Yaolin Jiang
ESAIM: M2AN, Forthcoming article
Received: 17 April 2025 / Revised: 15 December 2025 / Accepted: 03 January 2026
DOI: https://doi.org/10.1051/m2an/2026001

Convergence analysis and error estimates for the CSRK schemes to conserved gradient flows

Jingwei Sun, Xu Qian, Hong Zhang and Jiwei Zhang
ESAIM: M2AN, Forthcoming article
Received: 19 May 2025 / Revised: 02 December 2025 / Accepted: 21 December 2025
DOI: https://doi.org/10.1051/m2an/2025103

On the instabilities of naive FEM discretizations for PDEs with sign-changing coefficients

Martin Halla and Florian Oberender
ESAIM: M2AN, Forthcoming article
Received: 11 April 2025 / Revised: 12 November 2025 / Accepted: 21 December 2025
DOI: https://doi.org/10.1051/m2an/2025102

Maxwell à la Helmholtz: Electromagnetic scattering by 3D perfect electric conductors via Helmholtz integral operators

Juan Burbano-Gallegos, Carlos Perez-Arancibia and Catalin Turc
ESAIM: M2AN, Forthcoming article
Received: 26 May 2025 / Revised: 19 September 2025 / Accepted: 15 December 2025
DOI: https://doi.org/10.1051/m2an/2025101

Discretization and convergence of the ballistic Benamou-Brenier formulation of the porous medium and Burgers' equations

Jean-Marie Mirebeau and Erwan STAMPFLI
ESAIM: M2AN, Forthcoming article
Received: 06 April 2025 / Revised: 17 October 2025 / Accepted: 15 December 2025
DOI: https://doi.org/10.1051/m2an/2025100

Finite element discretization of nonlinear models of ultrasound heating

Benjamin Dörich, Julio Careaga and Vanja Nikolić
ESAIM: M2AN, Forthcoming article
Received: 14 February 2025 / Revised: 01 October 2025 / Accepted: 06 December 2025
DOI: https://doi.org/10.1051/m2an/2025099

Stability of lattice Boltzmann schemes for initial boundary value problems in raw formulation

Thomas Bellotti
ESAIM: M2AN, Forthcoming article
Received: 23 July 2025 / Revised: 24 October 2025 / Accepted: 03 December 2025
DOI: https://doi.org/10.1051/m2an/2025098

Numerical solution of two dimensional scalar conservation laws using compact implicit numerical schemes on Cartesian meshes

Peter Frolkovic and Dagmar Zakova
ESAIM: M2AN, Forthcoming article
Received: 28 August 2024 / Revised: 28 November 2025 / Accepted: 02 December 2025
DOI: https://doi.org/10.1051/m2an/2025097