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.
Gomez, S., Moiola, A., Perugia, I., Stocker, P. (2023). On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation. APPLIED MATHEMATICS LETTERS, 146(December 2023) [10.1016/j.aml.2023.108824].
On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
Sergio Gomez
Primo
;
2023
Abstract
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.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
