Space-time finite element method for Schrödinger equation and its conservation

DOI10.1007/s10483-006-0308-zzbMath1149.65313OpenAlexW1987149008MaRDI QIDQ944609

Qiong Tang, Chuan-miao Chen, Luo-Hua Liu

Publication date: 17 September 2008

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10483-006-0308-z

zbMATH Keywords

numerical resultsnonlinear Schrödinger equationfinite element methodsenergy conservation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Nonlinear ordinary differential equations and systems (34A34) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (4)

Superconvergence of Finite Element Approximations of the Two-Dimensional Cubic Nonlinear Schrödinger Equation ⋮ Runge-Kutta method, finite element method, and regular algorithms for Hamiltonian system ⋮ Superconvergence analysis of bi-\(k\)-degree rectangular elements for two-dimensional time-dependent Schrödinger equation ⋮ Mixed time discontinuous space-time finite element method for convection diffusion equations

Cites Work

• Finite-difference solutions of a non-linear Schrödinger equation
• A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
• The space-time finite element method for parabolic problems

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