A note on optimal \(H^1\)-error estimates for Crank-Nicolson approximations to the nonlinear Schrödinger equation

DOI10.1007/s10543-020-00814-3zbMath1460.35326arXiv1907.02782OpenAlexW3036819296MaRDI QIDQ2660595

Johan Wärnegård, Patrick Henning

Publication date: 31 March 2021

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.02782

zbMATH Keywords

finite elementsnonlinear Schrödinger equationsenergy conserving methodspriori error estimates

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (4)

A two-grid immersed finite element method with the Crank-Nicolson time scheme for semilinear parabolic interface problems ⋮ Optimal a priori error estimate of relaxation-type linear finite element method for nonlinear Schrödinger equation ⋮ Optimal convergence analysis of a linearized second-order BDF-PPIFE method for semi-linear parabolic interface problems ⋮ Superconvergence of time invariants for the Gross–Pitaevskii equation

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