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Works by Category

A list of papers, proceedings, and preprints by category.

Analysis

  1. Analysis and numerical analysis of the Helmholtz-Korteweg equation Patrick E. Farrell, Tim van Beeck, UZ arXiv, 2025.

Mathematical Physics and Modelling

  1. A Kinetic Interpretation of Thermomechanical Restrictions of Continua Patrick E. Farrell, Josef Málek, Ondřej Souček, UZ arXiv IJES, 2026.
  2. A Kinetic Theory Approach to Ordered Fluids José A. Carrillo, Patrick E. Farrell, Andrea Medaglia, UZ arXiv, 2025.
  3. Time-harmonic waves in Korteweg and nematic-Korteweg fluids Patrick E Farrell, UZ [PRE, arXiv (with corrections)], 2025.
  4. Kinetic Derivation of an Inviscid Compressible Leslie–Ericksen Equation for Rarified Calamitic Gases Patrick E Farrell, Giovanni Russo, UZ [SIAM MMS, arXiv], 2024.

Numerical Analysis

  1. Preconditioned normal equations for solving discretised partial differential equations Lorenzo Lazzarino, Yuji Nakatsukasa, UZ arXiv, 2025.
  2. A nodal ghost method based on variational formulation and regular square grid for elliptic problems on arbitrary domains in two space dimensions
    Clarissa Astuto, Daniele Boffi, Giovanni Russo, UZ [CMAME, arXiv], 2025.
  3. The Lightning Virtual Element Method for Self-adjoint Eigenvalue Problems
    Manuel Trezzi, UZ GIMC SIMAI Young 2024, 2025
  4. The High-Order Lightning Virtual Element Method
    Manuel Trezzi, UZ GIMC SIMAI Young 2024, 2025
  5. An adaptive mesh refinement strategy to ensure quasi-optimality of the conforming finite element method for the Helmholtz equation via T-coercivity
    Tim van Beeck, UZ arXiv, 2024.
  6. When rational functions meet virtual elements: the lightning virtual element method
    Manuel Trezzi, UZ [CALCOLO, arXiv, errata], 2024.
  7. A comparison of the Coco-Russo scheme and $\protect\mathghost$-FEM for elliptic equations in arbitrary domains
    Clarissa Astuto, Armando Coco, UZ ICIAM 2023, arXiv, 2024.
  8. PINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems UZ IFAC-PapersOnLine, 2022 [arXiv]

Scientific Computing

  1. ngsPETSc: A coupling between NETGEN/NGSolve and PETSc
    Jack Betteridge, Patrick E. Farrell, Matthias Hochsteger, Christopher Lackner, Joachim Schöberl, Stefano Zampini, UZ [JOSS, GitHub], 2024.
  2. PETScML: Second-Order Solvers for Training Regression Problems in Scientific Machine Learning
    Stefano Zampini, UZ, George Turkyyiah, David Elliot Keyes PASC’24, 2024 [arXiv]