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Article overview
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Convergence of a Strang splitting finite element discretization for the Schr"odinger-Poisson equation | | Winfried Auzinger
; Thomas Kassebacher
; Othmar Koch
; Mechthild Thalhammer
; | | Date: |
2 May 2016 | | Abstract: | Operator splitting methods combined with finite element spatial
discretizations are studied for time-dependent nonlinear Schr"odinger
equations. In particular, the Schr"odinger-Poisson equation under homogeneous
Dirichlet boundary conditions on a finite domain is considered. A rigorous
stability and error analysis is carried out for the second-order Strang
splitting method and conforming polynomial finite element discretizations. For
sufficiently regular solutions the classical orders of convergence are
retained, that is, second-order convergence in time and polynomial convergence
in space is proven. The established convergence result is confirmed and
complemented by numerical illustrations. | | Source: | arXiv, 1605.0437 | | Services: | Forum | Review | PDF | Favorites | |
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