5 papers · 1 filter
Structure-preserving Local Discontinuous Galerkin method for nonlinear cross-diffusion systems
Sergio Gómez, Ansgar Jüngel, Ilaria Perugia
We present and analyze a structure-preserving method for the approximation of solutions to nonlinear cross-diffusion systems, which combines a Local Discontinuous Galerkin spatial…
Asymptotic-preserving hybridizable discontinuous Galerkin method for the Westervelt quasilinear wave equation
Sergio Gómez, Mostafa Meliani
We discuss the asymptotic-preserving properties of a hybridizable discontinuous Galerkin method for the Westervelt model of ultrasound waves. More precisely, we show that the propo…
On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
Sergio Gómez, Andrea Moiola, Ilaria Perugia +1
We study the approximation properties of complex-valued polynomial Trefftz spaces for the -dimensional linear time-dependent Schrödinger equation. More precisely, we prove t…
Design and performance of a space-time virtual element method for the heat equation on prismatic meshes
Sergio Gómez, Lorenzo Mascotto, Ilaria Perugia
We present a space-time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategie…
A space-time DG method for the Schrödinger equation with variable potential
Sergio Gómez, Andrea Moiola
We present a space-time ultra-weak discontinuous Galerkin discretization of the linear Schrödinger equation with variable potential. The proposed method is well-posed and quasi-opt…