[HTML][HTML] Superconvergence analysis of finite element method for the time-dependent Schrödinger equation
In this paper, we consider the two-dimensional time-dependent Schrödinger equation.
Firstly, we use the rectangular Lagrange type finite element of order p to get a semi-discrete …
Firstly, we use the rectangular Lagrange type finite element of order p to get a semi-discrete …
An efficient meshless numerical method with the error estimate for two-dimensional Schrödinger equation
In this study, we present a capable meshfree numerical approach to numerical solving of the
two-dimensional Schrödinger equation (SE). Firstly, the radial point interpolation is obtained …
two-dimensional Schrödinger equation (SE). Firstly, the radial point interpolation is obtained …
A time-space adaptive method for the Schrödinger equation
K Kormann - Communications in Computational Physics, 2016 - cambridge.org
In this paper, we present a discretization of the time-dependent Schrödinger equation based
on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in …
on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in …
A posteriori error control and adaptivity for Crank–Nicolson finite element approximations for the linear Schrödinger equation
T Katsaounis, I Kyza - Numerische Mathematik, 2015 - Springer
We derive optimal order a posteriori error estimates for fully discrete approximations of linear
Schrödinger-type equations, in the L^ ∞ (L^ 2) L∞(L 2)-norm. For the discretization in time …
Schrödinger-type equations, in the L^ ∞ (L^ 2) L∞(L 2)-norm. For the discretization in time …
A Posteriori Error Analysis for Evolution Nonlinear Schrodinger Equations Up to the Critical Exponent
T Katsaounis, I Kyza - SIAM Journal on Numerical Analysis, 2018 - SIAM
We provide a posteriori error estimates in the L^∞(0,T;L^2(Ω))-norm for relaxation time
discrete and fully discrete schemes for a class of evolution nonlinear Schrödinger …
discrete and fully discrete schemes for a class of evolution nonlinear Schrödinger …
Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation
J Wang, Y Chen - Applied Mathematics and Mechanics, 2018 - Springer
Superconvergence has been studied for long, and many different numerical methods have
been analyzed. This paper is concerned with the problem of superconvergence for a two …
been analyzed. This paper is concerned with the problem of superconvergence for a two …
A time–space adaptive method for the Schrödinger equation
K Kormann - 2012 - diva-portal.org
In this paper, we present a discretization of the time-dependent Schrödinger equation based
on a Magnus–Lanczos time integrator and high-order Gauss–Lobatto finite elements in …
on a Magnus–Lanczos time integrator and high-order Gauss–Lobatto finite elements in …