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

Autori
Engstrom, Christian ; Giani, Stefano ; Grubišić, Luka

Izvornik
Journal of computational and applied mathematics (0377-0427) 400 (2022); 113652, 15

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Gross–Pitaevskii eigenvalue problem ; Discontinuous Galerkin finite element approximations ; Composite finite elements

Sažetak
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 modelled at the same time as macroscopic 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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