Recent articles published in 'ESAIM: Mathematical Modelling and Numerical Analysis'

Recent articles published in 'ESAIM: Mathematical Modelling and Numerical Analysis' https://www.esaim-m2an.org Recent articles published in 'ESAIM: Mathematical Modelling and Numerical Analysis' daily 1 2026-02-25T23:51:52Z EDP Sciences Copyright (c) EDP Sciences 2026 Copyright (c) EDP Sciences 2026 2822-7840 ESAIM: Mathematical Modelling and Numerical Analysis A quasi-interpolation operator yielding fully computable error bounds https://www.esaim-m2an.org/10.1051/m2an/2025091 Authors: Theophile Chaumont-Frelet and Martin Vohralík. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 1 Published online: 30/01/2026 Keywords: Finite element method ; interpolation operator ; stable projection ; error estimate ; guaranteed bound.65N30 ; 65N15 ; 65D05. A quasi-interpolation operator yielding fully computable error bounds Theophile Chaumont-Frelet Martin Vohralík Finite element method interpolation operator stable projection error estimate guaranteed bound 65N30 65N15 65D05 2026-01-30 text/html 10.1051/m2an/2025091 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-01-30 ESAIM: Mathematical Modelling and Numerical Analysis 1 60 Residual-based a posteriori error estimation for a space-time discontinuous Galerkin formulation of the Richards equation https://www.esaim-m2an.org/10.1051/m2an/2025094 Authors: Scott Congreve and Hyun-Geun Shin. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 25 Published online: 30/01/2026 Keywords: Richards equation ; a posteriori error estimates ; space-time discontinuous Galerkin ; adaptive refinement.65N15 ; 65N30 ; 65N50. Residual-based a posteriori error estimation for a space-time discontinuous Galerkin formulation of the Richards equation Scott Congreve Hyun-Geun Shin Richards equation a posteriori error estimates space-time discontinuous Galerkin adaptive refinement 65N15 65N30 65N50 2026-01-30 text/html 10.1051/m2an/2025094 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-01-30 ESAIM: Mathematical Modelling and Numerical Analysis 25 60 Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation https://www.esaim-m2an.org/10.1051/m2an/2025095 Authors: Jiayu Wan, Liu Liu and Zhenyi Zhu. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 51 Published online: 30/01/2026 Keywords: Linearized Boltzmann equation ; uncertainty quantification ; deep learning ; asymptotic-preserving neural networks ; hypocoercivity.35Q20 ; 68T07 ; 82C40 ; 65F99. Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation Jiayu Wan Liu Liu Zhenyi Zhu Linearized Boltzmann equation uncertainty quantification deep learning asymptotic-preserving neural networks hypocoercivity 35Q20 68T07 82C40 65F99 2026-01-30 text/html 10.1051/m2an/2025095 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-01-30 ESAIM: Mathematical Modelling and Numerical Analysis 51 60 Dynamic output-based feedback stabilizability for linear parabolic equations with memory https://www.esaim-m2an.org/10.1051/m2an/2025096 Authors: Arbaz Khan, Sumit Mahajan and Sérgio S. Rodrigues. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 83 Published online: 30/01/2026 Keywords: Parabolic equations with memory ; dynamic output-feedback stabilization ; continuous data assimilation ; positive kernels ; explicit feedback-input and output-injection operators.93D15 ; 93B52 ; 93-08 ; 93-10 ; 93C20. Dynamic output-based feedback stabilizability for linear parabolic equations with memory Arbaz Khan Sumit Mahajan Sérgio S. Rodrigues Parabolic equations with memory dynamic output-feedback stabilization continuous data assimilation positive kernels explicit feedback-input and output-injection operators 93D15 93B52 93-08 93-10 93C20 2026-01-30 text/html 10.1051/m2an/2025096 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-01-30 ESAIM: Mathematical Modelling and Numerical Analysis 83 60 Stability of lattice Boltzmann schemes for initial boundary value problems in raw formulation https://www.esaim-m2an.org/10.1051/m2an/2025098 Authors: Thomas Bellotti. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 143 Published online: 13/02/2026 Keywords: Strong/GKS-stability ; boundary conditions ; lattice Boltzmann schemes ; scalar hyperbolic equations ; Kreiss–Lopatinskii determinant ; characteristic boundary.65M12 ; 76M28 ; 65M06 ; 35L50 ; 35L65. Stability of lattice Boltzmann schemes for initial boundary value problems in raw formulation Thomas Bellotti Strong/GKS-stability boundary conditions lattice Boltzmann schemes scalar hyperbolic equations Kreiss–Lopatinskii determinant characteristic boundary 65M12 76M28 65M06 35L50 35L65 2026-02-13 text/html 10.1051/m2an/2025098 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-02-13 ESAIM: Mathematical Modelling and Numerical Analysis 143 60 Finite element discretization of nonlinear models of ultrasound heating https://www.esaim-m2an.org/10.1051/m2an/2025099 Authors: Julio Careaga, Benjamin Dörich and Vanja Nikolić. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 111 Published online: 13/02/2026 Keywords: Westervelt’s equation ; Kuznetsov’s equation ; wave-heat coupling ; finite element approximation ; a priori analysis.35L05 ; 35L72 ; 34A34. Finite element discretization of nonlinear models of ultrasound heating Julio Careaga Benjamin Dörich Vanja Nikolić Westervelt’s equation Kuznetsov’s equation wave-heat coupling finite element approximation a priori analysis 35L05 35L72 34A34 2026-02-13 text/html 10.1051/m2an/2025099 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-02-13 ESAIM: Mathematical Modelling and Numerical Analysis 111 60 Numerical solution of two dimensional scalar conservation laws using compact implicit numerical schemes on Cartesian meshes https://www.esaim-m2an.org/10.1051/m2an/2025097 Authors: Peter Frolkovič and Dagmar Žáková. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 247 Published online: 23/02/2026 Keywords: Compact implicit discretization ; high-resolution numerical method ; positive coefficients scheme ; advection equation ; Burgers equation.35L60 ; 35L65 ; 65M08 ; 65M12. Numerical solution of two dimensional scalar conservation laws using compact implicit numerical schemes on Cartesian meshes Peter Frolkovič Dagmar Žáková Compact implicit discretization high-resolution numerical method positive coefficients scheme advection equation Burgers equation 35L60 35L65 65M08 65M12 2026-02-23 text/html 10.1051/m2an/2025097 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-02-23 ESAIM: Mathematical Modelling and Numerical Analysis 247 60 Maxwell à la Helmholtz: Electromagnetic scattering by 3D perfect electric conductors via Helmholtz integral operators* https://www.esaim-m2an.org/10.1051/m2an/2025101 Authors: Juan Burbano-Gallegos, Carlos Pérez-Arancibia and Catalin Turc. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 273 Published online: 23/02/2026 Keywords: Electromagnetic scattering ; Maxwell equations ; Helmholtz equations ; boundary integral equations ; combined field formulations ; Nyström method.78A40 ; 65R20 ; 65N38 ; 65J10 ; 45B05. Maxwell à la Helmholtz: Electromagnetic scattering by 3D perfect electric conductors via Helmholtz integral operators* Juan Burbano-Gallegos Carlos Pérez-Arancibia Catalin Turc Electromagnetic scattering Maxwell equations Helmholtz equations boundary integral equations combined field formulations Nyström method 78A40 65R20 65N38 65J10 45B05 2026-02-23 text/html 10.1051/m2an/2025101 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-02-23 ESAIM: Mathematical Modelling and Numerical Analysis 273 60 Convergence analysis and error estimates for the CSRK schemes to conserved gradient flows https://www.esaim-m2an.org/10.1051/m2an/2025103 Authors: Jingwei Sun, Xu Qian, Hong Zhang and Jiwei Zhang. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 223 Published online: 13/02/2026 Keywords: Convergence and error estimate ; gradient flows ; convex splitting Runge–Kutta ; Cahn–Hilliard equation ; phase-field crystal equation.65M12 ; 65G40 ; 65L06 ; 35G20. Convergence analysis and error estimates for the CSRK schemes to conserved gradient flows Jingwei Sun Xu Qian Hong Zhang Jiwei Zhang Convergence and error estimate gradient flows convex splitting Runge–Kutta Cahn–Hilliard equation phase-field crystal equation 65M12 65G40 65L06 35G20 2026-02-13 text/html 10.1051/m2an/2025103 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-02-13 ESAIM: Mathematical Modelling and Numerical Analysis 223 60 On the instabilities of naive FEM discretizations for PDEs with sign-changing coefficients https://www.esaim-m2an.org/10.1051/m2an/2025102 Authors: Martin Halla and Florian Oberender. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 197 Published online: 13/02/2026 Keywords: sign-changing coefficients ; meta materials ; finite element method ; stability analysis.65N12 ; 65N30 ; 78M10. On the instabilities of naive FEM discretizations for PDEs with sign-changing coefficients Martin Halla Florian Oberender sign-changing coefficients meta materials finite element method stability analysis 65N12 65N30 78M10 2026-02-13 text/html 10.1051/m2an/2025102 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-02-13 ESAIM: Mathematical Modelling and Numerical Analysis 197 60 Two-scale integrators with high accuracy and long-time conservations for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime https://www.esaim-m2an.org/10.1051/m2an/2026001 Authors: Bin Wang, Zhen Miao and Yaolin Jiang. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60 , page 317 Published online: 23/02/2026 Keywords: Two-scale integrators ; high accuracy ; long time near conservation ; nonlinear Klein-Gordon equation ; modulated Fourier expansion.65M12 ; 65M15 ; 65M70. 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 Yaolin Jiang Two-scale integrators high accuracy long time near conservation nonlinear Klein-Gordon equation modulated Fourier expansion 65M12 65M15 65M70 2026-02-23 text/html 10.1051/m2an/2026001 ESAIM: Mathematical Modelling and Numerical Analysis Vol. 60(1) abstract m2an/2026/01 2026-02-23 ESAIM: Mathematical Modelling and Numerical Analysis 317 60