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http://hdl.handle.net/10397/93861
Title: | High-order mass- and energy-conserving SAV-Gauss collocation finite element methods for the nonlinear Schrödinger equation | Authors: | Feng, X Li, B Ma, S |
Issue Date: | 2021 | Source: | SIAM journal on numerical analysis, 2021, v. 59, no. 3, p. 1566-1591 | 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. | Keywords: | Error estimates High-order conserving schemes Mass- and energy-conservation Nonlinear Schrödinger equation SAV-Gauss collocation finite element method |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on numerical analysis | ISSN: | 0036-1429 | EISSN: | 1095-7170 | DOI: | 10.1137/20M1344998 | Rights: | © 2021 Society for Industrial and Applied Mathematics The following publication Feng, X., Li, B., & Ma, S. (2021). High-order Mass-and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation. SIAM Journal on Numerical Analysis, 59(3), 1566-1591 is available at https://doi.org/10.1137/20M1344998 |
Appears in Collections: | Journal/Magazine Article |
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