Cover Image

A structure-preserving relaxation Crank-Nicolson finite element method for the Schrödinger-Poisson equation

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Liu, Huini, Yi, Nianyu, Yin, Peimeng
Format:	Preprint
Published:	2024
Subjects:	Numerical Analysis 35Q55, 65M15, 65M60
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

A fully decoupled and structure-preserving relaxation Crank--Nicolson finite element method for Gross--Pitaevskii--Poisson model
by: Li, Dongqian, et al.
Published: (2026)

A second-order dynamical low-rank mass-lumped finite element method for the Allen-Cahn equation
by: Yang, Jun, et al.
Published: (2025)

Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schrödinger equation
by: Li, Hang, et al.
Published: (2025)

Optimal error estimates of the penalty finite element method for the unsteady Navier-Stokes equations with nonsmooth initial data
by: Bir, Bikram, et al.
Published: (2022)

On Error Estimates of the Crank-Nicolson-Polylinear Finite Element Method with the Discrete TBC for the Generalized Schrödinger Equation in an Unbounded Parallelepiped
by: Zlotnik, Alexander
Published: (2015)

Error analysis of a fully discrete structure-preserving finite element scheme for a diffuse-interface model of tumour growth
by: Soenjaya, Agus L., et al.
Published: (2025)

Optimal error bounds on the exponential integrator for dispersive equations with highly concentrated potential
by: Bal, Guillaume, et al.
Published: (2026)

Low regularity full error estimates for the cubic nonlinear Schrödinger equation
by: Ji, Lun, et al.
Published: (2023)

Low regularity error estimates for high dimensional nonlinear Schrödinger equations
by: Ji, Lun, et al.
Published: (2023)

Semi-discrete finite element approximation applied to Maxwell's equations in nonlinear media
by: Angermann, Lutz
Published: (2019)

Error estimates of the time-splitting methods for the nonlinear Schrödinger equation with semi-smooth nonlinearity
by: Bao, Weizhu, et al.
Published: (2023)

A two level approach for simulating Bose-Einstein condensates by localized orthogonal decomposition
by: Döding, Christian, et al.
Published: (2022)

The cubic nonlinear Schrödinger equation with rough potential
by: Mauser, Norbert J., et al.
Published: (2024)

Optimal error bounds on an exponential wave integrator Fourier spectral method for the logarithmic Schrödinger equation
by: Bao, Weizhu, et al.
Published: (2024)

Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time
by: Zhou, Han, et al.
Published: (2023)

Structure preserving discontinuous Galerkin approximation of a hyperbolic-parabolic system
by: Bause, Markus, et al.
Published: (2023)

Low regularity estimates of the Lie-Totter time-splitting Fourier spectral method for the logarithmic Schrödinger equation
by: Zhang, Xiaolong, et al.
Published: (2024)

Optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
by: Bao, Weizhu, et al.
Published: (2023)

Mixed finite element methods for the Landau--Lifshitz--Baryakhtar and the regularised Landau--Lifshitz--Bloch equations in micromagnetics
by: Soenjaya, Agus L.
Published: (2024)

Time splitting method for nonlinear Schrödinger equation with rough initial data in $L^2$
by: Choi, Hyung Jun, et al.
Published: (2023)

Efficient finite element methods for semiclassical nonlinear Schrödinger equations with random potentials
by: Li, Panchi, et al.
Published: (2025)

Stable $C^1$-conforming finite element methods for a class of nonlinear fourth-order evolution equations
by: Soenjaya, Agus L., et al.
Published: (2023)

An explicit and symmetric exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
by: Bao, Weizhu, et al.
Published: (2023)

Computing rough solutions of the stochastic nonlinear wave equation
by: Cao, Jiachuan, et al.
Published: (2024)

Optimal error bounds on the exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
by: Bao, Weizhu, et al.
Published: (2023)

An extended Fourier pseudospectral method for the Gross-Pitaevskii equation with low regularity potential
by: Bao, Weizhu, et al.
Published: (2023)

Optimal error bounds on the exponential wave integrator for nonlinear Schrödinger equations with highly singular potential
by: Bao, Weizhu, et al.
Published: (2026)

A Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip
by: Zlotnik, Alexander, et al.
Published: (2013)

Optimal error bounds on an exponential wave integrator Fourier spectral method for fractional nonlinear Schrödinger equations with low regularity potential and nonlinearity
by: Jia, Junqing, et al.
Published: (2024)

A Lawson-time-splitting extended Fourier pseudospectral method for the Gross-Pitaevskii equation with time-dependent low regularity potential
by: Lin, Bo, et al.
Published: (2024)

Error analysis of scalar auxiliary variable finite element methods for the Landau--Lifshitz--Bloch equation
by: Soenjaya, Agus L.
Published: (2026)

Neural network-enhanced $hr$-adaptive finite element algorithm for parabolic equations
by: Hao, Jiaxiong, et al.
Published: (2025)

Asymptotic-preserving and positivity-preserving discontinuous Galerkin method for the semiconductor Boltzmann equation in the diffusive scaling
by: Ding, Huan, et al.
Published: (2025)

Low regularity error estimates for the time integration of 2D NLS
by: Ji, Lun, et al.
Published: (2023)

Structure-preserving Local Discontinuous Galerkin method for nonlinear cross-diffusion systems
by: Gómez, Sergio, et al.
Published: (2024)

Error estimates of an exponential wave integrator for the nonlinear Schrödinger equation with singular potential
by: Bao, Weizhu, et al.
Published: (2025)

Explicit symmetric low-regularity integrators for the nonlinear Schrödinger equation
by: Feng, Yue, et al.
Published: (2024)

Computing nonlinear Schrödinger equations with Hermite functions beyond harmonic traps
by: Banica, Valeria, et al.
Published: (2025)

The Landau--Lifshitz--Bloch equation on polytopal domains: Unique existence and finite element approximation
by: Le, Kim-Ngan, et al.
Published: (2024)

A structure-preserving parametric finite element method with optimal energy stability condition for anisotropic surface diffusion
by: Li, Yifei, et al.
Published: (2025)