On accuracy of the mass-preserving DG method to multi-dimensional Schrödinger equations. (5th April 2018)

• Record Type: Journal Article
• Authors: Liu, Hailiang; Huang, Yunqing; Lu, Wenying; Yi, Nianyu
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 2(2019)
• Page Start: 760
• Page End: 791
• Publication Date: 2018-04-05
• Subjects: DG method -- Schrödinger equation -- numerical flux -- global projection -- superconvergence; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry012
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: In this paper, we present two approaches to the error analysis of a semidiscrete mass-preserving discontinuous Galerkin method, introduced by Lu, Huang and Liu (2015, Mass preserving direct discontinuous Galerkin methods for Schrödinger equations. J. Comp. Phys., 282, 210–226), for the solution of multi-dimensional Schrödinger equations. The first approach is based on an explicit global projection using tensor product polynomials on rectangular meshes. The L 2 error bound obtained is optimal, independent of the size of the flux parameter. The second approach is based on an implicit global projection using standard polynomials on arbitrary shape-regular meshes. The L 2 error bound obtained for this method is also optimal, but it is valid only when the flux parameter is sufficiently large. Numerical experiments are presented to demonstrate the theoretical results.