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Journal of Scientific Computing

Erschienen in:

25.07.2018

An Ultra-weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension

verfasst von: Anqi Chen, Fengyan Li, Yingda Cheng

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2019

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Abstract

In this paper, we develop an ultra-weak discontinuous Galerkin method to solve the one-dimensional nonlinear Schrödinger equation. Stability conditions and error estimates are derived for the scheme with a general class of numerical fluxes. The error estimates are based on detailed analysis of the projection operator associated with each individual flux choice. Depending on the parameters, we find out that in some cases, the projection can be defined element-wise, facilitating analysis. In most cases, the projection is global, and its analysis depends on the resulting \(2\times 2\) block-circulant matrix structures. For a large class of parameter choices, optimal a priori \(L^2\) error estimates can be obtained. Numerical examples are provided verifying theoretical results.

Vorheriger Artikel Correction to: A New Shifted Block GMRES Method with Inexact Breakdowns for Solving Multi-Shifted and Multiple Right-Hand Sides Linear Systems

Nächster Artikel Discontinuous Galerkin Methods with Optimal Accuracy for One Dimensional Linear PDEs with High Order Spatial Derivatives

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Titel: An Ultra-weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension
verfasst von: Anqi Chen
Fengyan Li
Yingda Cheng
Publikationsdatum: 25.07.2018
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0789-4

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