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Higher Order Composite DG approximations of Gross–Pitaevskii ground state: benchmark results and experiments

Engström, C. and Giani, S. and Grubišić, L. (2022) 'Higher Order Composite DG approximations of Gross–Pitaevskii ground state: benchmark results and experiments.', Journal of computational and applied mathematics., 400 . p. 113652.


Discontinuous Galerkin composite finite element methods (DGCFEM) are designed to tackle approximation problems on complicated domains. Partial differential equations posed on complicated domain are common when there are mesoscopic or local phenomena which need to be modeled at the same time as macropscopic phenomena. In this paper, an optical lattice will be used to illustrate the performance of the approximation algorithm for the ground state computation of a Gross-Pitaevskii equation, which is an eigenvalue problem with eigenvector nonlinearity. We will adapt the convergence results of Marcati and Maday 2018 to this particular class of discontinuous approximation spaces and benchmark the performance of the classic symmetric interior penalty hp-adaptive algorithm against the performance of the hp-DGCFEM.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives 4.0.
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Publisher statement:© 2021 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:08 May 2021
Date deposited:11 May 2021
Date of first online publication:27 July 2021
Date first made open access:27 January 2023

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