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HIGH-ORDER MASS- AND ENERGY-CONSERVING SAV-GAUSS COLLOCATION FINITE ELEMENT METHODS FOR THE NONLINEAR SCHRODINGER EQUATION.
- Source :
-
SIAM Journal on Numerical Analysis . 2021, Vol. 59 Issue 3, p1566-1591. 26p. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 59
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 151385863
- Full Text :
- https://doi.org/10.1137/20M1344998