Innovations in modeling and numerical methods for evolutionary PDEs: theory and applications

The numerical simulation of complex physical systems plays an instrumental role in modern scientific and engineering advancements. Within this framework, evolutionary partial differential equations (PDEs) are of interest in a wide range of physically relevant situations, such as computational fluid and solid mechanics, oceanography, plasma physics, materials science, and computational astrophysics. However, these types of PDEs are characterized by significant computational difficulties due to the vast range of involved spatial and temporal scales, as well as the complex mathematical structure underlying their behavior. Consequently, their solution remains a major challenge today and represents the central theme of the International HONOM cycle of conferences on High-order nonlinear numerical methods for evolutionary PDEs: theory and applications.