TY - JOUR
T1 - On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
AU - Gómez, Sergio
AU - Moiola, Andrea
AU - Perugia, Ilaria
AU - Stocker, Paul
N1 - Funding Information:
The authors have been funded by the Austrian Science Fund (FWF) through the projects F 65 and P 33477 (I. Perugia), by the Italian Ministry of University and Research, Italy through the PRIN project “NA-FROM-PDEs”, from PNRR-M4C2-I1.4-NC-HPC-Spoke6 . (A. Moiola, S. Gómez), and by DFG SFB 1456, Germany project 432680300 (P. Stocker). S. Gómez acknowledges the kind hospitality of the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), where part of this research was developed.
Publisher Copyright:
© 2023 The Author(s)
PY - 2023/12
Y1 - 2023/12
N2 - We study the approximation properties of complex-valued polynomial Trefftz spaces for the (d+1)-dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h-convergence rates as for polynomials of degree p in (d+1) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2p in d variables, and bases are easily constructed.
AB - We study the approximation properties of complex-valued polynomial Trefftz spaces for the (d+1)-dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h-convergence rates as for polynomials of degree p in (d+1) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2p in d variables, and bases are easily constructed.
KW - Discontinuous Galerkin method
KW - Extended Taylor polynomials
KW - Polynomial Trefftz space
KW - Schrödinger equation
KW - Ultra-weak formulation
UR - http://www.scopus.com/inward/record.url?scp=85168768343&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2023.108824
DO - 10.1016/j.aml.2023.108824
M3 - Article
AN - SCOPUS:85168768343
SN - 0893-9659
VL - 146
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
M1 - 108824
ER -