On the Conservation of Fractional Nonlinear Schrödinger Equation's Invariants by the Local Discontinuous Galerkin Method. - Paul Castillo 001; Sergio A. Gómez Macias (J. Sci. Comput., 2018)

Optimal stabilization and time step constraints for the forward Euler-Local Discontinuous Galerkin method applied to fractional diffusion equations. - Paul Castillo 001; Sergio Gómez 001 (J. Comput. Phys., 2019)

Improving the accuracy of LDG approximations on coarse meshes. - Paul Castillo 001; Sergio Gómez 001; Sergio Manzanarez (Math. Comput. Simul., 2019)

Conservative super-convergent and hybrid discontinuous Galerkin methods applied to nonlinear Schrödinger equations. - Paul Castillo 001; Sergio Gómez 001 (Appl. Math. Comput., 2020)

Interpolatory super-convergent discontinuous Galerkin methods for nonlinear reaction diffusion equations on three dimensional domains. - Paul Castillo 001; Sergio Gómez 001 (Commun. Nonlinear Sci. Numer. Simul., 2020)

On the Convergence of the Local Discontinuous Galerkin Method Applied to a Stationary One Dimensional Fractional Diffusion Problem. - Paul Castillo 001; Sergio Gómez 001 (J. Sci. Comput., 2020)

Conservative Local Discontinuous Galerkin method for the fractional Klein-Gordon-Schrödinger system with generalized Yukawa interaction. - Paul Castillo 001; Sergio Gómez 001 (Numer. Algorithms, 2020)

An interpolatory directional splitting-local discontinuous Galerkin method with application to pattern formation in 2D/3D. - Paul Castillo 001; Sergio Gómez 001 (Appl. Math. Comput., 2021)

Structure preserving - Field directional splitting difference methods for nonlinear Schrödinger systems. - Axi Aguilera; Paul Castillo 001; Sergio Gómez 001 (Appl. Math. Lett., 2021)

A unified framework of high order structure-preserving B-splines Galerkin methods for coupled nonlinear Schrödinger systems. - Paul Castillo 001; Sergio Gómez 001 (Comput. Math. Appl., 2021)

Conservative local discontinuous Galerkin methods for a generalized system of strongly coupled nonlinear Schrödinger equations. - Paul Castillo 001; Sergio Gómez 001 (Commun. Nonlinear Sci. Numer. Simul., 2021)

A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation. - Sergio Gómez 001; Andrea Moiola (SIAM J. Numer. Anal., 2022)

Design and performance of a space-time virtual element method for the heat equation on prismatic meshes. - Sergio Gómez 001; Lorenzo Mascotto; Ilaria Perugia (CoRR, 2023)

On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation. - Sergio Gómez 001; Andrea Moiola; Ilaria Perugia; Paul Stocker (Appl. Math. Lett., 2023)

Structure-preserving Local Discontinuous Galerkin method for nonlinear cross-diffusion systems. - Sergio Gómez 001; Ansgar Jüngel; Ilaria Perugia (CoRR, 2024)

Inf-sup stable space-time Local Discontinuous Galerkin method for the heat equation. - Sergio Gómez 001; Chiara Perinati; Paul Stocker (CoRR, 2024)

Space-Time Virtual Elements for the Heat Equation. - Sergio Gómez 001; Lorenzo Mascotto; Andrea Moiola; Ilaria Perugia (SIAM J. Numer. Anal., 2024)

A space-time DG method for the Schrödinger equation with variable potential. - Sergio Gómez 001; Andrea Moiola (Adv. Comput. Math., 2024)

A structure-preserving LDG discretization of the Fisher-Kolmogorov equation for modeling neurodegenerative diseases. - Paola F. Antonietti; Mattia Corti; Sergio Gómez 001; Ilaria Perugia (CoRR, 2025)