ESAIM: Mathematical Modelling and Numerical Analysis

A quasi-interpolation operator yielding fully computable error bounds

Théophile Chaumont-Frelet and Martin Vohralik

Received: 16 July 2025 / Revised: 10 October 2025 / Accepted: 17 October 2025

DOI: https://doi.org/10.1051/m2an/2025091

• PDF (629.1 KB)

Residual-based a posteriori error estimation for a space-time discontinuous Galerkin formulation of the Richards equation

Scott Congreve and Hyun-Geun Shin

Received: 27 January 2025 / Revised: 24 November 2025 / Accepted: 25 November 2025

DOI: https://doi.org/10.1051/m2an/2025094

• PDF (3.827 MB)

Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation

Jiayu Wan, Liu Liu and Zhenyi Zhu

Received: 05 March 2025 / Revised: 18 September 2025 / Accepted: 25 November 2025

DOI: https://doi.org/10.1051/m2an/2025095

• PDF (524.5 KB)

Dynamic output-based feedback stabilizability for linear parabolic equations with memory

Arbaz Khan, Sumit Mahajan and Sergio s. Rodrigues

Received: 03 April 2025 / Revised: 18 September 2025 / Accepted: 27 November 2025

DOI: https://doi.org/10.1051/m2an/2025096

• PDF (1.665 MB)

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

Thomas Bellotti

Received: 23 July 2025 / Revised: 24 October 2025 / Accepted: 03 December 2025

DOI: https://doi.org/10.1051/m2an/2025098

• PDF (1.503 MB)

Finite element discretization of nonlinear models of ultrasound heating

Benjamin Dörich, Julio Careaga and Vanja Nikolić

Received: 14 February 2025 / Revised: 01 October 2025 / Accepted: 06 December 2025

DOI: https://doi.org/10.1051/m2an/2025099

• PDF (3.363 MB)

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

Received: 11 June 2025 / Revised: 02 December 2025 / Accepted: 19 January 2026

DOI: https://doi.org/10.1051/m2an/2026008

• PDF (617.1 KB)

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

Juan Burbano-Gallegos, Carlos Perez-Arancibia and Catalin Turc

Received: 26 May 2025 / Revised: 19 September 2025 / Accepted: 15 December 2025

DOI: https://doi.org/10.1051/m2an/2025101

• PDF (22.68 MB)

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

Jingwei Sun, Xu Qian, Hong Zhang and Jiwei Zhang

Received: 19 May 2025 / Revised: 02 December 2025 / Accepted: 21 December 2025

DOI: https://doi.org/10.1051/m2an/2025103

• PDF (543.6 KB)

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

Martin Halla and Florian Oberender

Received: 11 April 2025 / Revised: 12 November 2025 / Accepted: 21 December 2025

DOI: https://doi.org/10.1051/m2an/2025102

• PDF (1.105 MB)

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

Sebastiano Boscarino and Seung Yeon Cho

Received: 22 August 2025 / Revised: 23 December 2025 / Accepted: 06 January 2026

DOI: https://doi.org/10.1051/m2an/2026002

• PDF (834.5 KB)

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

Received: 17 April 2025 / Revised: 15 December 2025 / Accepted: 03 January 2026

DOI: https://doi.org/10.1051/m2an/2026001

• PDF (1.575 MB)

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

David Mora, Jesus Vellojin and Nitesh Verma

Received: 11 June 2024 / Revised: 07 December 2025 / Accepted: 13 January 2026

DOI: https://doi.org/10.1051/m2an/2026005

• PDF (21.27 MB)

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

Tomas Roubicek

Received: 19 April 2025 / Revised: 07 December 2025 / Accepted: 08 January 2026

DOI: https://doi.org/10.1051/m2an/2026003

• PDF (686.7 KB)

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

Nicolas Crouseilles, Giacomo Dimarco and Saurav Samantaray

Received: 30 December 2024 / Revised: 10 December 2025 / Accepted: 08 January 2026

DOI: https://doi.org/10.1051/m2an/2026004

• PDF (4.894 MB)

A generalized framework for higher-order Localized Orthogonal Decomposition methods

Moritz Hauck, Alexei Lozinski and Roland Maier

Received: 30 July 2025 / Revised: 02 December 2025 / Accepted: 13 January 2026

DOI: https://doi.org/10.1051/m2an/2026006

• PDF (1.418 MB)

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

Jean-Marie Mirebeau and Erwan STAMPFLI

Received: 06 April 2025 / Revised: 17 October 2025 / Accepted: 15 December 2025

DOI: https://doi.org/10.1051/m2an/2025100

• PDF (3.281 MB)

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

Received: 14 February 2025 / Revised: 14 December 2025 / Accepted: 15 January 2026

DOI: https://doi.org/10.1051/m2an/2026007

• PDF (4.446 MB)

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

Peter Frolkovic and Dagmar Zakova

Received: 28 August 2024 / Revised: 28 November 2025 / Accepted: 02 December 2025

DOI: https://doi.org/10.1051/m2an/2025097

• PDF (2.998 MB)