High-order mass- And energy-conserving sav-gauss collocation finite element methods for the nonlinear schrÖdinger equation

Xiaobing Feng, Buyang Li, Shu Ma

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)

Abstract

A family of arbitrarily high-order fully discrete space-time finite element methods are proposed for the nonlinear Schrödinger equation based on the scalar auxiliary variable formulation, which consists of a Gauss collocation temporal discretization and the finite element spatial discretization. The proposed methods are proved to be well-posed and conserving both mass and energy at the discrete level. An error bound of the form O(hp + τk+1) in the L(0, T; H1)-norm is established, where h and τ denote the spatial and temporal mesh sizes, respectively, and (p, k) is the degree of the space-time finite elements. Numerical experiments are provided to validate the theoretical results on the convergence rates and conservation properties. The effectiveness of the proposed methods in preserving the shape of a soliton wave is also demonstrated by numerical results.

Original languageEnglish
Pages (from-to)1566-1591
Number of pages26
JournalSIAM Journal on Numerical Analysis
Volume59
Issue number3
DOIs
Publication statusE-pub ahead of print - 9 Jun 2021

Keywords

  • Error estimates
  • High-order conserving schemes
  • Mass- and energy-conservation
  • Nonlinear Schrödinger equation
  • SAV-Gauss collocation finite element method

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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