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Advanced applications & analysis of Trefftz methods

The goal of this project is to turn Trefftz methods into a versatile and widely usable tool in numerical simulation.

Project details
🎓 Funding program ESPRIT
⏳ Status ongoing
🚀 Start July 1, 2024
🏁 End June 30, 2027
💶 Funding amount 340819 €
🏢 Host institution University of Vienna
👤 Principal Investigator Paul Stocker
🌐 Grant website fwf.ac.at
🔗 Grant DOI 10.55776/ESP4389824

Trefftz Workshop 2026

To mark 100 years since Erich Trefftz’s seminal 1926 paper, the Trefftz Workshop 2026: A Century of Trefftz Methods took place in Vienna from 7-9 September 2026. The project helped fund the workshop, which I co-organized; it was a wonderful few days of inspiring talks and discussions.

Publications related to this project

  1. Comparing domain decomposition preconditioners for non-conforming Helmholtz discretizations
    Moritz Gallauner, Emile Parolin, PS, Igor Voulis
    arXiv:2608.07326, 2026

  2. Embedded Trefftz DG method for steady Navier-Stokes flow. Part II: Nonlinear problem
    PS, Igor Voulis, Christoph Lehrenfeld, Philip L. Lederer
    arXiv:2606.13219, 2026

  3. Embedded Trefftz DG method for steady Navier-Stokes flow. Part I: Oseen linearization
    PS, Igor Voulis, Christoph Lehrenfeld, Philip L. Lederer
    arXiv:2606.13229, 2026

  4. Embedded Trefftz DG method for reaction-diffusion problems on anisotropic meshes
    Sergio Gómez, Chiara Perinati, PS, Igor Voulis
    arXiv:2606.03845, 2026

  5. A discontinuous Galerkin method for elliptic-hyperbolic equations
    Chiara Perinati, Lise-Marie Imbert-Gérard, Andrea Moiola, PS
    arXiv:2604.06910, 2026

  6. Embedded Trefftz DG method for the Helmholtz equation
    PS, Igor Voulis
    arXiv:2603.13034, 2026

  7. Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions
    Philip L. Lederer, Christoph Lehrenfeld, PS, Igor Voulis
    arXiv:2412.00806, 2024

  8. Inf-sup stable space-time local discontinuous Galerkin method for the heat equation
    Sergio Gómez, Chiara Perinati, PS
    J. Sci. Comput., 2025

  9. Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems
    Lise-Marie Imbert-Gérard, Andrea Moiola, Chiara Perinati, PS
    IMA J. Numer. Anal., 2025