Advances in least squares and Galerkin methods

Organized by Thomas Führer/Norbert Heuer/Michael Karkulik

02

Computational electromagnetism

Organized by Ana Alonso/Dolores Gómez/Rodolfo Rodriguez

Computational methods play a central role in the analysis and simulation of a broad range of electromagnetic phenomena and applications, supporting the development of advanced devices and a deeper understanding of the underlying physical processes. Many applications also involve the interaction of electromagnetic fields with other physical phenomena, giving rise to challenging multiphysics problems. This minisymposium aims to provide a forum for researchers in the field of computational electromagnetism to discuss recent developments, exchange ideas and discuss current and emerging challenges in the field. Contributions may address, among other topics, mathematical modelling, discretisation techniques, mathematical and numerical analysis, control and optimisation, multiphysics approaches, computational methodologies and applications.

1 scheduled talks

Authors (speaker underlined)	Title	Abstract
TBA TBA	TBA	N/A

03

Functional analysis tools in numerical methods for PDEs

Organized by Michele Botti/Lorenzo Mascotto

This minisymposium focuses on the application of functional analysis tools to numerical methods for partial differential equations (PDEs). Topics of interest include continuous and discrete functional inequalities, nonstandard and fractional function spaces, well-posedness of PDEs in Banach spaces, inf-sup stability conditions for mixed formulations, and finite element complexes. The session aims to present recent advances in these areas and to discuss their role in proving the stability and convergence of numerical schemes

1 scheduled talks

Authors (speaker underlined)	Title	Abstract
TBA TBA	TBA	N/A

04

Integral Equations in Coupled Physical Systems

Organized by Christopher Cooper/Ignacio Labarca/Elwin van 't Wout

Integral-equation formulations of partial differential equations provide a powerful framework for accurate numerical simulation of coupled physical systems. Their strengths include the natural handling of unbounded domains, reduced meshing requirements, and efficient treatment of high-frequency wave problems and point-charge forcing terms. These methods are used in a wide range of scientific and engineering applications, including acoustics, elastodynamics, and electrostatics. This minisymposium will present recent developments in the numerical analysis and implementation of volume and boundary integral equations, high-performance algorithms for large-scale dense matrix computations, and the numerical simulation of physical phenomena in coupled and complex domains.

0 scheduled talks

Authors (speaker underlined)	Title	Abstract
To be announced

05

Mathematical modelling in biomedicine

Organized by Felipe Galarce/Argyrios Petras

Mathematical models based on partial differential equations have become accurate and powerful tools for describing physiological and pathophysiological processes, as well as for predicting the effect of therapies and medical devices. Their personalisation gives rise to digital twins that can contribute to diagnosis, treatment planning and the improvement of clinical outcomes. Building such digital twins typically relies on multiphysics and multiscale models, together with the calibration of their constitutive laws. Clinical and experimental validation, and the ability to compute solutions within clinically feasible times, are essential for these models to be translated into practice. This minisymposium brings together researchers working on the formulation, calibration and simulation of PDE based models in biomedicine, and on the translation of these models towards clinical and industrial application.

0 scheduled talks

Authors (speaker underlined)	Title	Abstract
To be announced

06

Neural networks for partial differential equations

Organized by Juan Manuel Cárdenas/Paulina Sepúlveda

This mini-symposium explores the use of artificial neural networks as computational tools for solving partial differential equations. It aims to bring together researchers working at the intersection of scientific computing, numerical analysis, and machine learning to discuss recent methodological advances and practical applications. Particular emphasis will be placed on novel neural network architectures and learning strategies tailored to PDE problems. The session seeks to foster collaboration and exchange of ideas while highlighting the growing potential of neural network-based approaches to transform the modeling and numerical solution of complex PDE systems.

1 scheduled talks

Authors (speaker underlined)	Title	Abstract
TBA TBA	TBA	N/A

07

Non-standard finite elements and linear solvers –– Mini-symposium on the occasion of Guido Kanschat's 60th birthday

Organized by Daniel Arndt/Andreas Rupp/Natasha Sharma

Over the past three decades, finite element methods beyond the classical conforming framework — discontinuous Galerkin, mixed, divergence-conforming, and hybridizable discretizations — have evolved from analytical curiosities into indispensable tools for the simulation of transport, flow, and multiphysics problems. Their success rests on two pillars that must be developed hand in hand: discretizations with built-in structure preservation, such as local conservation, exact incompressibility, and pressure robustness, and fast linear solvers, including multilevel and domain decomposition methods with specially tailored smoothers, that make these discretizations competitive at scale. A third, often underappreciated pillar is software: generic, extensible finite element libraries have turned methods that once required heroic implementation efforts into everyday research infrastructure. The talks will survey recent advances in non-standard discretizations, robust preconditioning and multigrid, matrix-free and high-performance implementations, software development, and applications ranging from radiative transfer to poroelasticity.

0 scheduled talks