Research

S. Gómez, C. Perinati, P. Stocker, and I. Voulis (2026).
Embedded Trefftz DG method for reaction–diffusion problems on anisotropic meshes. Submitted.
[Preprint] [Bibtex]

S. Gómez, D. Hewett, and A. Moiola (2026).
A discontinuous Galerkin method with fractal elements. Submitted.
[Preprint] [Bibtex]

L. Beirão da Veiga, S. Gómez, I. Perugia, and E. Zampa (2026).
Robust H(curl)-based finite element methods for the incompressible MHD system. Submitted.
[Preprint] [Bibtex]

S. Gómez (2026).
Galerkin-type time discretizations for parabolic and hyperbolic problems: stability and a priori error analysis. Submitted.
[Preprint] [Bibtex]

M. Corti and S. Gómez (2026).
On the Compact Discontinuous Galerkin method for polytopal meshes. Submitted.
[Preprint] [Bibtex]

M. Ferrari and S. Gómez (2025).
A matrix-based approach to the stability of a space–time isogeometric method for the linear Schödinger equation. Submitted.
[Preprint] [Bibtex]

P.-F. Antonietti, M. Corti, S. Gómez, and I. Perugia (2026).
Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems.
Accepted for publication in Mathematics of Computation.
[Preprint] [Bibtex]

S. Gómez (2026).
A note on the compactness properties of discontinuous Galerkin time discretizations of nonlinear evolution problems.
Nonlinear Analysis: Real World Applications, 92, 104639.
[Preprint] [Article] [Bibtex]

S. Gómez, C. Perinati, and P. Stocker (2026).
Inf⁠–sup stable space–time Local Discontinuous Galerkin method for the heat equation.
Journal of Scientific Computing, 106(1), 22.
[Preprint] [Article] [Bibtex]

P.-F. Antonietti, M. Corti, S. Gómez, and I. Perugia (2026).
A structure-preserving LDG discretization of the Fisher-Kolmogorov equation for modeling neurodegenerative diseases.
Mathematics and Computers in Simulation, 241(A), 351–366.
[Preprint] [Article] [Bibtex]

S. Gómez, A. Jüngel, and I. Perugia (2026).
Structure-preserving Local Discontinuous Galerkin method for nonlinear cross-diffusion systems.
Available online in  IMA  Journal of Numerical Analysis.
[Preprint] [Article] [Bibtex]

S. Gómez (2025).
A variational approach to the analysis of the continuous space–time FEM for the wave equation.
Available online in Mathematics of Computation.
[Preprint] [Article] [Bibtex]

S. Gómez and V. Nikolić (2025).
Combined DG–CG finite element method for the Westervelt equation.
Available online in IMA Journal of Numerical Analysis.
[Preprint] [Article] [Bibtex]

L. Beirão da Veiga, F. Dassi, and S. Gómez (2025).
Fully and semi-implicit robust space–time DG methods for the incompressible Navier–Stokes equations.
Mathematical Models and Methods in Applied Sciences (M3AS), 35(12), 2561–2609.
[Preprint] [Article] [Bibtex]

L. Beirão da Veiga, F. Dassi, and S. Gómez (2025).
SUPG-stabilized time-DG finite and virtual elements for the time-dependent advection–diffusion equation.
Computer Methods in Applied Mechanics and Engineering, 436, 117722.
[Preprint] [Article] [Bibtex]

S. Gómez and M. Meliani (2025).
Asymptotic-preserving hybridizable discontinuous Galerkin method for the Westervelt quasilinear wave equation.
ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 59(2), 613–641.
[Preprint] [Article] [Bibtex]

S. Gómez and A. Moiola (2024).
A space–time DG method for the Schrödinger equation with variable potential.
Advances in Computational Mathematics, 50(2), 15.
[Preprint] [Article] [Bibtex]

S. Gómez, L. Mascotto, and I. Perugia (2024).
Design and performance of a space–time virtual element method for the heat equation on prismatic meshes.
Computer Methods in Applied Mechanics and Engineering, 418(A), 116491.
[Preprint] [Article] [Bibtex]

S. Gómez, L. Mascotto, A. Moiola, and I. Perugia (2024).
Space–time virtual elements for the heat equation.
SIAM Journal on Numerical Analysis, 62(1), 199–228.
[Preprint] [Article] [Bibtex]

S. Gómez, A. Moiola, I. Perugia, and P. Stocker (2023).
On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation.
Applied Mathematics Letters, 146, 108824.
[Preprint] [Article] [Bibtex]

S. Gómez (2022).
High-order interpolatory Serendipity Virtual Element Method for semilinear parabolic problems.
Calcolo, 59(3), 25.
[Preprint] [Article] [Bibtex]

S. Gómez and A. Moiola (2022).
A space–time Trefftz Discontinuous Galerkin method for the linear Schrödinger equation.
SIAM Journal on Numerical Analysis, 60(2), 688–714.
[Preprint] [Article] [Bibtex]

P. Castillo and S. Gómez (2021).
A unified framework of high order structure-preserving B-splines Galerkin methods for coupled nonlinear Schrödinger systems.
Computers & Mathematics with Applications, 102, 45–53.
[Article] [Bibtex]

P. Castillo and S. Gómez (2021).
Conservative Local Discontinuous Galerkin methods for a generalized system of strongly coupled nonlinear Schrödinger equations.
Communications in Nonlinear Science and Numerical Simulation, 99, 105836.
[Article] [Bibtex]

A. Aguilera, P. Castillo, and S. Gómez (2021).
Structure preserving - field directional splitting difference methods for nonlinear Schrödinger systems.
Applied Mathematics Letters, 119, 107211.
[Article] [Bibtex]

P. Castillo and S. Gómez (2021).
An interpolatory directional splitting-Local Discontinuous Galerkin method with application to pattern formation in 2D/3D.
Applied Mathematics and Computation, 397, 125984.
[Article] [Bibtex]

P. Castillo and S. Gómez (2020).
On the convergence of the Local Discontinuous Galerkin method applied to a stationary one dimensional fractional diffusion problem.
Journal of Scientific Computing, 85(2), 32.
[Article] [Bibtex]

P. Castillo and S. Gómez (2020).
Interpolatory super-convergent discontinuous Galerkin methods for nonlinear reaction diffusion equations on three dimensional domains.
Communications in Nonlinear Science and Numerical Simulation, 90, 105388.
[Article] [Bibtex]

P. Castillo and S. Gómez (2020).
Conservative super-convergent and hybrid discontinuous Galerkin methods applied to nonlinear Schrödinger equations.
Applied Mathematics and Computation, 371, 124950.
[Article] [Bibtex]

P. Castillo and S. Gómez (2020).
Conservative Local Discontinuous Galerkin method for the fractional Klein-Gordon-Schrödinger system  with generalized Yukawa interaction.
Numerical Algorithms, 84(1), 407–425.
[Article] [Bibtex]

P. Castillo and S. Gómez (2019).
Optimal stabilization and time step constraints for the forward Euler-Local Discontinuous Galerkin method applied to fractional diffusion equations.
Journal of Computational Physics, 394(C), 503–521.
[Article] [Bibtex]

P. Castillo, S. Gómez, and S. Manzanarez (2019).
Improving the accuracy of LDG approximations on coarse grids.
Mathematics and Computers in Simulation, 156, 310–326.
[Article] [Bibtex]

P. Castillo and S. Gómez (2018).
On the conservation of fractional nonlinear Schrödinger equation's invariants by the Local Discontinuous Galerkin method.
Journal of Scientific Computing, 77(3), 1444–1467.
[Article] [Bibtex]

A. Aguilera, P. Castillo, and S. Gómez (2022).
High order conservative Finite Difference method for a class of nonlinear Schrödinger systems.
Revista Mexicana de Física E, 19(1), 1–14.
[Article] [Bibtex]

P. Castillo and S. Gómez (2019).
Von Neumann analysis for the Local Discontinuous Galerkin method in 1D.
Revista Integración, temas de matemáticas, 37(2), 199–217.
[Article] [Bibtex]

P. Castillo and S. Gómez (2018).
Conservation of the nonlinear Schrödinger equation invariants by the LDG method.
Revista Mexicana de Física E, 64(1), 52–60.
[Article] [Bibtex]

P. Castillo and S. Gómez (2017).
Efficiency of the LDG method to approximate the solution of the Bratu and Troesch problems.
Revista de la escuela de Física, UNAH, 5(2), 39–46.
[Article]