Convergence of a finite element scheme for the two-dimensional time-dependent Schrödinger equation in a long strip

DOI10.1016/j.cam.2010.01.042zbMath1191.65118OpenAlexW1988190663WikidataQ57692491 ScholiaQ57692491MaRDI QIDQ966091

Jicheng Jin, Xiao-Nan Wu

Publication date: 27 April 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.01.042

zbMATH Keywords

stabilityconvergencenumerical examplestime-dependent Schrödinger equationartificial boundary conditionfinite element method in spaceCrank-Nicolson scheme in time

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (12)

Superconvergence of Finite Element Approximations of the Two-Dimensional Cubic Nonlinear Schrödinger Equation ⋮ Error Estimates of the Crank-Nicolson-Polylinear FEM with the Discrete TBC for the Generalized Schrödinger Equation in an Unbounded Parallelepiped ⋮ A fast BDF2 Galerkin finite element method for the one-dimensional time-dependent Schrödinger equation with artificial boundary conditions ⋮ Fast artificial boundary method for the heat equation on unbounded domains with strip tails ⋮ Two-grid method for the two-dimensional time-dependent Schrödinger equation by the finite element method ⋮ Superconvergence Analysis of Bilinear Finite Element for the Nonlinear Schrodinger Equation on the Rectangular Mesh ⋮ Superconvergence analysis of finite element method for the time-dependent Schrödinger equation ⋮ Superconvergence analysis of bi-\(k\)-degree rectangular elements for two-dimensional time-dependent Schrödinger equation ⋮ Two-grid finite volume element method for the time-dependent Schrödinger equation ⋮ Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrödinger equation with cubic nonlinearity ⋮ On a Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip ⋮ Two-Grid Crank-Nicolson Finite Volume Element Method for the Time-Dependent Schrödinger Equation

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