Research
Research Interests:
Discontinuous Galerkin methods.
Virtual element methods.
Space-time methods for evolution PDEs.
Structure-preserving numerical methods for nonlinear PDEs.
Numerical approximation of fractional PDEs.
Scientific collaborators:
Paul Castillo, University of Puerto Rico at Mayagüez.
Ansgar Jüngel, TU Wien.
Lorenzo Mascotto, University of Milano-Bicocca.
Mostafa Meliani, Radboud University.
Andrea Moiola, University of Pavia.
Ilaria Perugia, University of Vienna.
Paul Stocker, University of Vienna.
Preprints
S. Gómez, A. Jüngel, and I. Perugia (2024).
Structure-preserving Local Discontinuous Galerkin method for nonlinear cross-diffusion systems. [Preprint]S. Gómez and M. Meliani (2024).
Asymptotic-preserving hybridizable discontinuous Galerkin method for the Westervelt quasilinear wave equation. Submitted. [Preprint]
Papers in international journals (in english)
S. Gómez and A. Moiola (2024).
A space–time DG method for the Schrödinger equation with variable potential.
Advances in Computational Mathematics, 50, 15. [Preprint] [Article]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]S. Gómez, L. Mascotto, A. Moiola, and I. Perugia (2024).
Space-time virtual elements for the heat equation.
SIAM Journal of Numerical Analysis, 62(1), 199-228. [Preprint] [Article]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(C), 108824. [Preprint] [Article]S. Gómez (2022).
High-order interpolatory Serendipity Virtual Element Method for semilinear parabolic problems.
Calcolo, 59(3), 25. [Preprint] [Article]S. Gómez and A. Moiola (2022).
A space-time Trefftz Discontinuous Galerkin method for the linear Schrödinger equation.
SIAM Journal of Numerical Analysis, 60(2), 688 - 714. [Preprint] [Article]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(C), 45-53. [Article]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(C), 105836. [Article]A. Aguilera, P. Castillo, and S. Gómez (2021).
Structure preserving - field directional splitting difference methods for nonlinear Schrödinger systems.
Applied Mathematics Letters, 119(C), 107211. [Article]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(C), 125984. [Article]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). [Article]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(C), 105388. [Article]P. Castillo and S. Gómez (2020).
Conservative super-convergent and hybrid discontinuous Galerkin methods applied to nonlinear Schrödinger equations.
Applied Mathematics and Computation, 371(C), 124950. [Article]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, 407-425. [Article]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]P. Castillo, S. Gómez, and S. Manzanarez (2018).
Improving the accuracy of LDG approximations on coarse grids.
Mathematics and Computers in Simulation, 156, 310-326. [Article]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]
Papers in Latin-American journals (in spanish)
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]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]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]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]