Portrait of Gonçalo Pena

Gonçalo Pena

Assistant Professor

Department of Mathematics
University of Coimbra

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About

Assistant Professor, Department of MathematicsFaculty of Sciences and Technology · University of Coimbra · Member of CMUC

I work on the numerical analysis of partial differential equations, mainly the stability and convergence of finite difference and finite element methods on nonuniform grids, with applications to drug delivery.

PhD in Applied Mathematics and Scientific Computing, EPFL (2009). I develop Bramble.jl, a Julia package for these methods.

Research interests

  • Numerical analysis of PDEs
  • Convergence of discrete variational PINNs
  • Supraconvergence and superconvergence
  • Finite differences on nonuniform grids
  • Drug delivery models
  • Non-Fickian diffusion

Research

7 publicationsDrug delivery modellingDrug transport driven by electric fields, temperature and viscoelastic polymers. 7 publicationsConvergence of FDM/FEMStability and second-order convergence of FDM/FEM on nonuniform grids. 6 publicationsFluid–structure interaction & hemodynamicsHigh-order methods for Navier–Stokes in moving domains and blood flow. 7 publicationsNon-Fickian diffusion & memoryDiffusion with memory in time and space.

Software

Bramble.jlJulia package · since 2024

Supraconvergent finite difference discretizations on nonuniform Cartesian grids.

Second-order finite differences on nonuniform grids. Move the slider to re-solve the Poisson problem.

v3.44.1MIT licenceJulia 1.13+
GitHub Documentation

Recent publications

All publications

Current teaching

All courses
  • BSc in Aerospace Engineering; BSc in Electrical and Computer EngineeringAnálise Matemática IMathematical Analysis I
  • BSc in Aerospace Engineering; BSc in Electrical and Computer EngineeringAnálise Matemática IIMathematical Analysis II
  • BSc in Artificial Intelligence and Data ScienceÁlgebra Linear Numérica e Cálculo CientíficoNumerical Linear Algebra and Scientific Computing
  • PhD in MathematicsMatemática ComputacionalComputational Mathematics
  • Since 2010Previous courses and lecture notes11 earlier courses

Recent talks

24 talks since 2001
  • Sep 2026 · InvitedSimulation of High-Intensity Ultrasound for Therapeutic Applications2026 Summer School in Computational Biology
  • Sep 2026 · InvitedHigh intensity ultrasound: applications and simulationEncontro Nacional da Sociedade Portuguesa de Matemática 2026
  • Jul 2026The linearized Westervelt–Pennes bioheat system: numerical analysis and simulationEquadiff 2026
  • Sep 2025 · InvitedSimulation of High-Intensity Ultrasound for Therapeutic Applications2025 Summer School in Computational Biology

Contact

Email

goncalo.pena@uc.pt

Office

Office 5.4, Department of Mathematics
Largo D. Dinis, 3000-143 Coimbra, Portugal

Affiliations

Profiles