Preface to the Focused Issue on High-Order Numerical Methods for Evolutionary PDEs
Arturo Hidalgo, Michael Dumbser, Eleuterio F. Toro

Neural Network-Based Limiter with Transfer Learning
Rémi Abgrall, Maria Han Veiga

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability
R. Abgrall, J. Nordström, P. Öffner, S. Tokareva

A High-Order Conservative Semi-Lagrangian Solver for 3D Free Surface Flows with Sediment Transport on Voronoi Meshes (Open Access)
Matteo Bergami, Walter Boscheri, Giacomo Dimarco

Stationarity Preservation Properties of the Active Flux Scheme on Cartesian Grids  
Wasilij Barsukow

Construction of Conservative Numerical Fluxes for the Entropy Split Method
Björn Sjögreen, H. C. Yee

A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods  
Johannes Markert, Gregor Gassner, Stefanie Walch

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method  (Open Access)
Jonas Zeifang, Andrea Beck

A Posteriori Stabilized Sixth-Order Finite Volume Scheme with Adaptive Stencil Construction: Basics for the 1D Steady-State Hyperbolic Equations
Gaspar J. Machado, Stéphane Clain, Raphaël Loubère

AENO: a Novel Reconstruction Method in Conjunction with ADER Schemes for Hyperbolic Equations  
Eleuterio F. Toro, Andrea Santacá, Gino I. Montecinos, Morena Celant, Lucas O. Müller

Multi-dimensional Simulation of Phase Change by a 0D-2D Model Coupling via Stefan Condition
Adrien Drouillet, Romain Le Tellier, Raphaël Loubère, Mathieu Peybernes, Louis Viot

Numerical Simulation of Bed Load and Suspended Load Sediment Transport Using Well-Balanced Numerical Schemes
J. C. González-Aguirre, J. A. González-Vázquez, J. Alavez-Ramírez, R. Silva, M. E. Vázquez-Cendón

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations 
Jean-Luc Guermond, Bojan Popov, Laura Saavedra

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media 
Paula Luna, Arturo Hidalgo