Advances in Numerical Analysis and Spectral Approximation for Partial Differential Equations

Organizado por Felipe Lepe/Gonzalo Rivera/Jesús Vellojín

The numerical analysis and spectral approximation of partial differential equations (PDEs) constitute an active and vibrant area of research in modern applied mathematics. Accurate approximation of eigenvalues and eigenfunctions plays a crucial role in numerous engineering and scientific applications, such as structural design of bridges and buildings, noise reduction devices, plate dynamics, and stability analysis in coupled problems. Alongside well-established techniques such as finite element methods (FEM), discontinuous Galerkin (DG), virtual element methods (VEM), and least-squares formulations, recent years have witnessed major breakthroughs in next-generation numerical schemes. These include stabilization-free VEM frameworks, reduced basis techniques, and non-conforming methods designed to provide guaranteed upper and lower bounds for the discrete spectrum. This minisymposium aims to bring together researchers to discuss recent theoretical and computational advances in the numerical solution of PDE spectral problems, with a particular interest in applications to continuum mechanics and related disciplines.

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02

Advances in least squares and Galerkin methods

Organizado por Thomas Führer/Norbert Heuer/Michael Karkulik

03

Computational electromagnetism

Organizado por 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 charlas programadas

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04

Discontinuous Galerkin, Mixed, and Hybridizable Methods: Recent Advances in Theory, Computation, and Applications

Organizado por Manuel Sánchez-Uribe/Patrick Vega

This mini-symposium concentrates on recent developments in the numerical approximation of partial differential equations using discontinuous Galerkin (DG) and mixed finite element methods, together with their hybridizable variants. These frameworks share foundational properties such as local conservation and structure-preserving discretizations. Hybridizable discontinuous Galerkin (HDG) methods emerge at this intersection, combining mixed formulations with a suitable stabilization that enables static condensation and efficient implementations. From this common root, the field has grown into a broad and active area of research that embraces modern computational paradigms. We invite contributions to this mini-symposium across its full range: the design of new discretizations and stabilization strategies for DG, mixed, and HDG methods; structure-preserving and locally conservative formulations; a posteriori error estimation, adaptivity, and multiscale methods; efficient linear and nonlinear solvers and preconditioners; implementations on emerging computer architectures, including GPU and high-performance computing; robust shock-capturing techniques; and applications in fluid mechanics, solid mechanics, electromagnetics, and other areas of computational science and engineering. By bridging rigorous numerical analysis with cutting-edge computational science, this session aims to foster discussions on the future trajectory of these versatile methods.

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05

Discretization Aspects in PDE-Constrained and Shape Optimization

Organizado por Roland Herzog

06

Functional analysis tools in numerical methods for PDEs

Organizado por 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

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07

Innovations in Modeling and Numerical Methods for Evolutionary PDEs: from theory to applications

Organizado por Davide Ferrari/Elena Gaburro/Mária Lukácová-Medvidová/Michal Žeravý

This minisymposium focuses on recent advances in the modeling and numerical solution of evolution- ary PDEs arising in a wide range of physically relevant applications, including computational fluid and solid mechanics, oceanography, plasma physics, geophysics, materials science, mathematical biology, computational astrophysics, and biodiversity modeling. Evolutionary PDEs pose major computational challenges because of the wide range of spatial and tem- poral scales involved and the complex mathematical structures governing their behavior. The minisym- posium will present advanced mathematical models, robust and efficient numerical algorithms, and new theoretical developments. Particular attention will be devoted to modern high-order schemes on Cartesian and unstructured grids, structure-preserving numerical methods and PDE models, Lagrangian methods, mesh generation and optimization techniques, kinetic methods, and challenging real-world applications.

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08

Innovative numerical methods for multiphysics problems

Organizado por Fleurianne Bertrand/Daniele Boffi

09

Integral Equations in Coupled Physical Systems

Organizado por 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.

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10

Inverse Problems and Data Assimilation: Numerical and Computational Challenges

Organizado por Jorge Aguayo

Inverse problems involve recovering model parameters or full states from partial or noisy observations. They are related to problems in optimal control, image processing, shape optimization, and local operator inversion, among other areas. Several problems derived from applied sciences, such as fluid mechanics, biomedicine, geology, and engineering, to name a few, give rise to inverse problems that require a multidisciplinary approach. This minisymposium focuses on theoretical and numerical aspects of complex models, particularly partial differential equations, and on developing new methodologies to solve data-driven inverse problems based on numerical methods of PDEs, optimal control, shape optimization, and artificial neural networks. This also includes interactions with other fields facing inverse problems such as scientific machine learning and model order reduction, where cheaper surrogates are used to repeatedly evaluate evolution or stationary models to estimate quantities that are otherwise hidden from the measurements.

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11

Iterative methods for strongly nonlinear PDE's

Organizado por Mohamed Ben Abdelouahab/Koondanibha Mitra/Anna Peruso

Numerically solving strongly nonlinear PDEs can be challenging both in the choice of discretization and in the design of iterative methods, as classical linearization strategies often require significant adaptation to remain effective. This is particularly relevant for a wide range of nonlinear PDEs, including fully nonlinear and degenerate problems such as Monge-Ampère, Pucci-type, and Hamilton-Jacobi-Bellman equations. This minisymposium focuses on iterative methods for strongly nonlinear PDEs, including Newton-type methods, fixed-point and continuation strategies, nonlinear least-squares methods, alternating projections, preconditioning, and adaptive iterative techniques. Particular attention will be given to the interaction between discretization and nonlinear solvers, as well as to the analysis and computational performance of these approaches.

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12

Mathematical modelling in biomedicine

Organizado por 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.

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13

Mixed Formulations and Numerical Methods for Coupled Problems in Elastic and Poroelastic Media

Organizado por Sergio Caucao/Cristian Inzunza

This minisymposium focuses on mixed formulations in Hilbert and Banach frameworks and numerical methods for coupled problems arising in elastic, porous, and poroelastic media. Topics of interest include mixed and fully mixed finite element methods for elasticity, thermoelasticity, poroelasticity, and flow in porous media, as well as coupled models involving Brinkman, Biot, Brinkman-Forchheimer, and related systems. Particular emphasis will be given to formulations based on vorticity, pseudostress, and skewsymmetric structures, together with the development and analysis of stable finite element discretizations. Other topics include well-posedness, parameter-robust stability, a priori and a posteriori error analysis, and convergence of numerical schemes

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14

Neural networks for partial differential equations

Organizado por 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 charlas programadas

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TBA TBA	TBA	N/A

15

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

Organizado por 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.

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16

Numerical PDE-constrained optimization

Organizado por Enrique Otárola/Abner Salgado

17

Numerical methods for anisotropic problems

Organizado por Umberto Zerbinati/Tim van Beeck

Anisotropy arises across many applications, through strongly varying material coecients, through solution features with pronounced scale separation such as boundary and interior layers, or through the anisotropic meshes used to resolve them. Examples include wave propagation in layered media, nematic liquid crystals and nematoacoustics, and thin elastic structures. Solving these problems numerically is challenging, because the resulting operators are often degenerate or non- symmetric, and the meshes needed to capture layers and interfaces stretch well beyond the usual shape-regularity and minimum-angle conditions. This minisymposium brings together recent advances in the numerical analysis of anisotropic prob- lems and their applications. The talks combine rigorous numerical analysis with computational practice, spanning well-posedness and discrete stability theory, anisotropic and graded meshes, and applications.

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18

Numerical methods for brain multiphysics

Organizado por Paola Antonietti/Alberto Girelli/Kent-André Mardal/Ricardo Ruiz-Baier

This special session focuses on recent advances in the rigorous numerical analysis and adaptive discretization of coupled multiphysics problems in brain biomechanics, centered on brain poromechanics, cerebrospinal fluid (CSF) dynamics, and interstitial fluid (ISF) transport. While mathematical modeling establishes the governing coupled continuum systems, translating these tissue dynamics into stable computational frameworks presents severe analytical and algorithmic challenges. The session emphasizes numerical analysis over empirical modeling, targeting foundational properties such as novel discretizations, parameter-robust stability, well-posedness, and rigorous convergence rates for multi-field Biot, Stokes-Darcy-Biot, and other multiphysics formulations. Key theoretical and algorithmic topics include mixed-dimensional coupling approaches, non-matching interface discretizations, domain decomposition techniques across physical boundaries, and adaptivity. The mini-symposium aims to bring together numerical analysts and computational scientists to exchange innovative discretization strategies, tackle open theoretical problems, and establish a rigorous mathematical foundation for the computational multiphysics of the brain.

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19

Polytopal Methods for PDEs: Applications in Continuum Mechanics

Organizado por Lourenço Beirão da Veiga/David Mora/Alberth Silgado/Giuseppe Vacca

In this minisymposium, we aim to bring together researchers working on the theoretical analysis and applications of polytopal methods for partial differential equations arising in continuum mechanics. These methods have received considerable attention in recent years due to their inherent flexibility in handling complex geometries, and their ability to accommodate general polygonal and polyhedral meshes. We invite participants to present their latest results and insights on the development, analysis, and application of polytopal methods to a broad range of problems in continuum mechanics. The minisymposium will provide an opportunity to discuss recent advances, identify emerging challenges, and foster collaboration and knowledge exchange within this rapidly developing area.

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20

Recent developments in Numerical Methods for Hyperbolic Conservation Laws with Applications

Organizado por Eduardo Abreu/John Pérez/Luis-Miguel Villada Osorio

21

Scientific computing and iterative algorithms for solving PDEs

Organizado por Nicolas Barnafi

22

Session of Communications

Organizado por Verónica Anaya

Minisymposia confirmados