Publications

1. Embedded Trefftz DG method for the Helmholtz equation

   PS, Igor Voulis

   arXiv:2603.13034, 2026 [ preprint , bibtex ]
   @article{SV_ARXIV_2026, author = {Stocker, Paul and Voulis, Igor}, title = {Embedded {T}refftz {DG} method for the {H}elmholtz equation}, journal = {arXiv preprint arXiv:2603.13034}, year = {2026}, doi = {10.48550/arXiv.2603.13034}, url = {https://arxiv.org/abs/2603.13034}, }

2. 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 [ preprint , bibtex ]
   @article{LLSV_ARXIV_2024, author = {Lederer, Philip L. and Lehrenfeld, Christoph and Stocker, Paul and Voulis, Igor}, title = {Embedded {T}refftz {DG} framework for the analysis of discretizations with local-global decompositions}, journal = {arXiv preprint arXiv:2412.00806}, year = {2024}, doi = {10.48550/arXiv.2412.00806}, url = {https://arxiv.org/abs/2412.00806}, }

3. Inf-sup stable space-time local discontinuous Galerkin method for the heat equation

   Sergio Gómez, Chiara Perinati, PS

   J. Sci. Comput., 2025 [ preprint , bibtex ]
   @article{GPS_JSC_2025, author = {Gómez, Sergio and Perinati, Chiara and Stocker, Paul}, title = {Inf-sup stable space-time local discontinuous {G}alerkin method for the heat equation}, journal = {Journal of Scientific Computing}, year = {2025}, volume = {106}, number = {1}, pages = {22}, doi = {10.1007/s10915-025-03121-7}, url = {https://doi.org/10.1007/s10915-025-03121-7}, }

4. 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 [ preprint , bibtex ]
   @article{IMPS_IMAJNA_2025, author = {Imbert-Gérard, Lise-Marie and Moiola, Andrea and Perinati, Chiara and Stocker, Paul}, title = {Polynomial quasi-{T}refftz {DG} for {PDE}s with smooth coefficients: elliptic problems}, journal = {IMA Journal of Numerical Analysis}, year = {2025}, pages = {drae094}, doi = {10.1093/imanum/drae094}, url = {https://doi.org/10.1093/imanum/drae094}, }

5. Sparsity comparison of polytopal finite element methods

   Christoph Lehrenfeld, PS, Maximilian Zienecker

   Proc. Appl. Math. Mech., 2024 [ preprint , bibtex ]
   @article{LSZ_PAMM_2024, author = {Lehrenfeld, Christoph and Stocker, Paul and Zienecker, Maximilian}, title = {Sparsity comparison of polytopal finite element methods}, journal = {PAMM}, year = {2024}, volume = {24}, number = {3}, pages = {e202400150}, doi = {10.1002/pamm.202400150}, url = {https://doi.org/10.1002/pamm.202400150}, }

6. Trefftz discontinuous Galerkin discretization for the Stokes problem

   Philip L. Lederer, Christoph Lehrenfeld, PS

   Numer. Math., 2024 [ preprint , bibtex ]
   @article{LLS_NM_2024, author = {Lederer, Philip L. and Lehrenfeld, Christoph and Stocker, Paul}, title = {Trefftz discontinuous {G}alerkin discretization for the {S}tokes problem}, journal = {Numerische Mathematik}, year = {2024}, doi = {10.1007/s00211-024-01404-z}, url = {https://doi.org/10.1007/s00211-024-01404-z}, }

7. On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation

   Sergio Gómez, Andrea Moiola, Ilaria Perugia, PS

   Appl. Math. Lett., 2023 [ preprint , bibtex ]
   @article{GMPS_AML_2023, author = {Gómez, Sergio and Moiola, Andrea and Perugia, Ilaria and Stocker, Paul}, title = {On polynomial {T}refftz spaces for the linear time-dependent {S}chrödinger equation}, journal = {Applied Mathematics Letters}, year = {2023}, volume = {146}, pages = {108824}, doi = {10.1016/j.aml.2023.108824}, url = {https://doi.org/10.1016/j.aml.2023.108824}, }

8. Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems

   Fabian Heimann, Christoph Lehrenfeld, PS, Henry Wahl

   ESAIM: M2AN, 2023 [ preprint , bibtex ]
   @article{HLSW_M2AN_2022, author = {Heimann, Fabian and Lehrenfeld, Christoph and Stocker, Paul and von Wahl, Henry}, title = {Unfitted {T}refftz discontinuous {G}alerkin methods for elliptic boundary value problems}, journal = {ESAIM: M2AN}, year = {2023}, doi = {10.1051/m2an/2023064}, url = {https://doi.org/10.1051/m2an/2023064}, }

9. A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun's equation

   Martin Halla, Christoph Lehrenfeld, PS

   IMA J. Numer. Anal., 2025 [ preprint, slides , bibtex ]
   @article{HLS_IMAJNA_2025, author = {Halla, Martin and Lehrenfeld, Christoph and Stocker, Paul}, title = {A new {T}-compatibility condition and its application to the discretization of the damped time-harmonic {G}albrun's equation}, journal = {IMA Journal of Numerical Analysis}, year = {2025}, pages = {draf071}, doi = {10.1093/imanum/draf071}, url = {https://doi.org/10.1093/imanum/draf071}, }

10. Robust finite element discretizations for a simplified Galbrun's equation

    Tilman Alemán, Martin Halla, Christoph Lehrenfeld, PS

    ECCOMAS 2022, 2022 [ preprint , bibtex ]
    @inproceedings{AHLS_ECCOMAS_2022, author = {Alemán, Tilman and Halla, Martin and Lehrenfeld, Christoph and Stocker, Paul}, title = {Robust finite element discretizations for a simplified {G}albrun's equation}, booktitle = {ECCOMAS 2022}, year = {2022}, doi = {10.23967/eccomas.2022.206}, url = {https://www.scipedia.com/public/Aleman_et_al_2022a}, }

11. NGSTrefftz: add-on to NGSolve for Trefftz methods

    PS

    J. Open Source Softw., 2022 [ slides , bibtex ]
    @article{S_JOSS_2022, author = {Stocker, Paul}, title = {{NGSTrefftz}: add-on to {NGSolve} for {T}refftz methods}, journal = {Journal of Open Source Software}, year = {2022}, volume = {7}, number = {71}, pages = {4135}, doi = {10.21105/joss.04135}, url = {https://doi.org/10.21105/joss.04135}, }

12. Embedded Trefftz discontinuous Galerkin methods

    Christoph Lehrenfeld, PS

    Int. J. Numer. Methods Eng., 2023 [ preprint , bibtex ]
    @article{LS_IJMNE_2023, author = {Lehrenfeld, Christoph and Stocker, Paul}, title = {Embedded {T}refftz discontinuous {G}alerkin methods}, journal = {International Journal for Numerical Methods in Engineering}, year = {2023}, volume = {124}, number = {17}, pages = {3637--3661}, doi = {10.1002/nme.7258}, url = {https://doi.org/10.1002/nme.7258}, }

13. A space-time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients

    Lise-Marie Imbert-Gérard, Andrea Moiola, PS

    Math. Comp., 2022 [ preprint , bibtex ]
    @article{IGMS_MC_2021, author = {Imbert-Gérard, Lise-Marie and Moiola, Andrea and Stocker, Paul}, title = {A space-time quasi-{T}refftz {DG} method for the wave equation with piecewise-smooth coefficients}, journal = {Mathematics of Computation}, year = {2022}, doi = {10.1090/mcom/3786}, url = {https://doi.org/10.1090/mcom/3786}, }

14. An entropy structure preserving space-time formulation for cross-diffusion systems: analysis and Galerkin discretization

    Marcel Braukhoff, Ilaria Perugia, PS

    SIAM J. Numer. Anal., 2022 [ preprint, slides , bibtex ]
    @article{BPS_SINUM_2022, author = {Braukhoff, Marcel and Perugia, Ilaria and Stocker, Paul}, title = {An entropy structure preserving space-time formulation for cross-diffusion systems: analysis and {G}alerkin discretization}, journal = {SIAM Journal on Numerical Analysis}, year = {2022}, volume = {60}, number = {1}, pages = {364--395}, doi = {10.1137/20M1360086}, url = {https://doi.org/10.1137/20M1360086}, }

15. Tent pitching and Trefftz-DG method for the acoustic wave equation

    Ilaria Perugia, Joachim Schöberl, PS, Christoph Wintersteiger

    Comput. Math. Appl., 2020 [ preprint , bibtex ]
    @article{PSSW_CMA_2020, author = {Perugia, Ilaria and Sch{\"o}berl, Joachim and Stocker, Paul and Wintersteiger, Christoph}, title = {Tent pitching and {T}refftz-{DG} method for the acoustic wave equation}, journal = {Computers \& Mathematics with Applications}, year = {2020}, volume = {79}, number = {10}, pages = {2987--3000}, doi = {10.1016/j.camwa.2020.01.006}, url = {https://doi.org/10.1016/j.camwa.2020.01.006}, }

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